Problem 10101
| ODE |
\[ \boxed {y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}=-x a} \] |
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program solution |
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Maple solution | \[ \ln \left (x \right )-\frac {\left (\int _{}^{\frac {y \left (x \right )}{x}}\frac {\textit {\_g}^{2} \left (\left (\left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {1}{3}}-2\right ) \sqrt {3}+3 \left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {1}{3}} \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} \sqrt {3}-\ln \left (\frac {1}{\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+2+\cos \left (2 \textit {\_Z} \right )}\right )-6 c_{1} -6 \left (\int \frac {\left (\frac {a}{\textit {\_g}^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2}}{\textit {\_g}^{3}+a}d \textit {\_g} \right )\right )\right )\right )}{\textit {\_g}^{3}+a}d \textit {\_g} \right ) \sqrt {3}}{6}-c_{2} = 0 \] |
Problem 10102
| ODE |
\[ \boxed {y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}=x a +b} \] |
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program solution |
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Maple solution | \[ y \left (x \right ) = \operatorname {RootOf}\left (\sqrt {3}\, b \left (\int _{}^{\textit {\_Z}}-\frac {\left (-\left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} \sqrt {3}\, b +2 \sqrt {3}\, a -3 b \left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {1}{3}} \tan \left (\operatorname {RootOf}\left (-2 b^{2} \left (-\frac {a}{\textit {\_g}^{3} b^{3}}\right )^{\frac {2}{3}} \textit {\_g}^{2} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (a^{2} \textit {\_Z}^{3}-1\right )}{\sum }\frac {\ln \left (\textit {\_g} -\textit {\_R} \right )}{\textit {\_R}^{2}}\right )+2 \textit {\_Z} \sqrt {3}\, a^{2}-\ln \left (\frac {1}{\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+2+\cos \left (2 \textit {\_Z} \right )}\right ) a^{2}-6 c_{1} a^{2}\right )\right )\right ) \textit {\_g}^{2}}{\textit {\_g}^{3} a^{2}-1}d \textit {\_g} \right ) a -6 \ln \left (a x +b \right ) b +6 c_{2} a \right ) \left (a x +b \right ) \] |
Problem 10103
| ODE |
\[ \boxed {\left (y^{2}+1\right ) y^{\prime \prime }+\left (1-2 y\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ y = \tan \left (\ln \left (c_{1} c_{2} +c_{1} x \right )\right ) \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= -i \\ y \left (x \right ) &= i \\ y \left (x \right ) &= \tan \left (\ln \left (c_{1} x +c_{2} \right )\right ) \\ \end{align*} |
Problem 10104
| ODE |
\[ \boxed {\left (y^{2}+1\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2}=0} \] |
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program solution |
\[ y = c_{2} \sqrt {-\frac {1}{c_{1}^{2} c_{2}^{2}+2 c_{1}^{2} c_{2} x +c_{1}^{2} x^{2}-1}}\, c_{1} +x \sqrt {-\frac {1}{c_{1}^{2} c_{2}^{2}+2 c_{1}^{2} c_{2} x +c_{1}^{2} x^{2}-1}}\, c_{1} \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= -i \\ y \left (x \right ) &= i \\ y \left (x \right ) &= \sqrt {-\frac {1}{c_{1}^{2} x^{2}+2 c_{1} c_{2} x +c_{2}^{2}-1}}\, \left (c_{1} x +c_{2} \right ) \\ \end{align*} |
Problem 10105
| ODE |
\[ \boxed {\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y^{\prime } y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= \sqrt {-x} \\ y \left (x \right ) &= -\sqrt {-x} \\ \frac {-c_{1} y \left (x \right )+\ln \left (x +y \left (x \right )^{2}\right )+c_{2} +2}{y \left (x \right )} &= 0 \\ \end{align*} |
Problem 10106
| ODE |
\[ \boxed {\left (y^{2}+x^{2}\right ) y^{\prime \prime }-\left ({y^{\prime }}^{2}+1\right ) \left (y^{\prime } x -y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \tan \left (\operatorname {RootOf}\left (\cos \left (\textit {\_Z} \right )^{2} {\mathrm e}^{-\frac {2 \left (\textit {\_Z} c_{1} i+i \textit {\_Z} +c_{2} c_{1} -c_{2} \right )}{-1+c_{1}}}-x^{2}\right )\right ) x \\ \end{align*} |
Problem 10107
| ODE |
\[ \boxed {\left (y^{2}+x^{2}\right ) y^{\prime \prime }-2 \left ({y^{\prime }}^{2}+1\right ) \left (y^{\prime } x -y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \frac {c_{1} -\sqrt {c_{1}^{2}+\left (4 i c_{2} x +2\right ) c_{1} -4 c_{2}^{2} x^{2}-4 i c_{2} x +1}+1}{2 c_{2}} \\ y \left (x \right ) &= \frac {c_{1} +1+\sqrt {c_{1}^{2}+\left (4 i c_{2} x +2\right ) c_{1} -4 c_{2}^{2} x^{2}-4 i c_{2} x +1}}{2 c_{2}} \\ \end{align*} |
Problem 10108
| ODE |
\[ \boxed {2 y \left (1-y\right ) y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+y \left (1-y\right ) y^{\prime } f \left (x \right )=0} \] |
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program solution |
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Maple solution | \[ y \left (x \right ) = \frac {4 \,{\mathrm e}^{c_{1} \left (\int {\mathrm e}^{-\frac {\left (\int f \left (x \right )d x \right )}{2}}d x \right )} c_{2}^{2}+4 c_{2} +{\mathrm e}^{-c_{1} \left (\int {\mathrm e}^{-\frac {\left (\int f \left (x \right )d x \right )}{2}}d x \right )}}{8 c_{2}} \] |
Problem 10109
| ODE |
\[ \boxed {2 y \left (1-y\right ) y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} \int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_b} \left (\int \frac {h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{3} \textit {\_b}^{2}}d \textit {\_b} +c_{1} \right )}\, \left (\textit {\_b} -1\right )}d \textit {\_b} -x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_b} \left (\int \frac {h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{3} \textit {\_b}^{2}}d \textit {\_b} +c_{1} \right )}\, \left (\textit {\_b} -1\right )}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10110
| ODE |
\[ \boxed {2 y \left (y-1\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (y-1\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right )=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10111
| ODE |
\[ \boxed {-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right )=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10112
| ODE |
\[ \boxed {3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} -\sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\left (\textit {\_b} \left (\textit {\_b} -1\right )\right )^{\frac {1}{3}} \textit {\_b} \left (\textit {\_b} -1\right ) \left (2 \left (\int \frac {h \left (\textit {\_b} \right )}{\textit {\_b}^{2} \left (\textit {\_b} -1\right )^{2} \left (\textit {\_b} \left (\textit {\_b} -1\right )\right )^{\frac {1}{3}}}d \textit {\_b} \right )-3 c_{1} \right )}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \sqrt {3}\, \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\left (\textit {\_b} \left (\textit {\_b} -1\right )\right )^{\frac {1}{3}} \textit {\_b} \left (\textit {\_b} -1\right ) \left (2 \left (\int \frac {h \left (\textit {\_b} \right )}{\textit {\_b}^{2} \left (\textit {\_b} -1\right )^{2} \left (\textit {\_b} \left (\textit {\_b} -1\right )\right )^{\frac {1}{3}}}d \textit {\_b} \right )-3 c_{1} \right )}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10113
| ODE |
\[ \boxed {\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} \int _{}^{y \left (x \right )}\frac {{\mathrm e}^{-6 \textit {\_b}}}{\sqrt {-2 \left (\int \frac {{\mathrm e}^{-12 \textit {\_b}} h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{7}}d \textit {\_b} \right )+c_{1}}\, \left (\textit {\_b} -1\right )^{3}}d \textit {\_b} -x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {{\mathrm e}^{-6 \textit {\_b}}}{\sqrt {-2 \left (\int \frac {{\mathrm e}^{-12 \textit {\_b}} h \left (\textit {\_b} \right )}{\left (\textit {\_b} -1\right )^{7}}d \textit {\_b} \right )+c_{1}}\, \left (\textit {\_b} -1\right )^{3}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10114
| ODE |
\[ \boxed {a y \left (y-1\right ) y^{\prime \prime }+\left (y b +c \right ) {y^{\prime }}^{2}+h \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} a \left (\int _{}^{y \left (x \right )}\frac {\textit {\_b}^{-\frac {c}{a}} \left (\textit {\_b} -1\right )^{\frac {c +b}{a}}}{\sqrt {-2 a \left (-\frac {c_{1} a}{2}+\int \textit {\_b}^{\frac {-a -2 c}{a}} h \left (\textit {\_b} \right ) \left (\textit {\_b} -1\right )^{\frac {2 c +2 b -a}{a}}d \textit {\_b} \right )}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ -a \left (\int _{}^{y \left (x \right )}\frac {\textit {\_b}^{-\frac {c}{a}} \left (\textit {\_b} -1\right )^{\frac {c +b}{a}}}{\sqrt {-2 a \left (-\frac {c_{1} a}{2}+\int \textit {\_b}^{\frac {-a -2 c}{a}} h \left (\textit {\_b} \right ) \left (\textit {\_b} -1\right )^{\frac {2 c +2 b -a}{a}}d \textit {\_b} \right )}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10115
| ODE |
\[ \boxed {a y \left (y-1\right ) y^{\prime \prime }-\left (-1+a \right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime }=0} \] |
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program solution |
\[ \int _{}^{y}\frac {\left (\textit {\_a} \left (\textit {\_a} -1\right )\right )^{\frac {1}{a}}}{\left (\left (-1\right )^{-\frac {1}{a}} \textit {\_a}^{\frac {1}{a}} \operatorname {hypergeom}\left (\left [\frac {1}{a}, 1-\frac {1}{a}\right ], \left [1+\frac {1}{a}\right ], \textit {\_a}\right ) f +c_{1} \right ) \textit {\_a} \left (\textit {\_a} -1\right )}d \textit {\_a} = x +c_{2} \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= 1 \\ y \left (x \right ) &= 0 \\ c_{1} {\mathrm e}^{-\frac {f x}{a}}-c_{2} +\int _{}^{y \left (x \right )}\frac {\left (\textit {\_a} \left (\textit {\_a} -1\right )\right )^{\frac {1}{a}}}{\textit {\_a} \left (\textit {\_a} -1\right )}d \textit {\_a} &= 0 \\ \end{align*} |
Problem 10116
| ODE |
\[ \boxed {a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime }=0} \] |
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program solution |
\[ \int _{}^{y}\frac {b \left (\textit {\_a} -1\right )^{-\frac {-1+b}{b}}}{\textit {\_a} \left (-1\right )^{-\frac {1}{b}} \operatorname {hypergeom}\left (\left [\frac {1}{a}, 1-\frac {1}{b}\right ], \left [1+\frac {1}{a}\right ], \textit {\_a}\right ) f +b \,\textit {\_a}^{\frac {-1+a}{a}} c_{1}}d \textit {\_a} = x +c_{2} \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= 1 \\ y \left (x \right ) &= 0 \\ c_{1} {\mathrm e}^{-\frac {f x}{b a}}+\int _{}^{y \left (x \right )}\textit {\_a}^{\frac {-a +1}{a}} \left (\textit {\_a} -1\right )^{\frac {1-b}{b}}d \textit {\_a} -c_{2} &= 0 \\ \end{align*} |
Problem 10117
| ODE |
\[ \boxed {x y^{2} y^{\prime \prime }=a} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= \frac {c_{1} x \left (81 c_{1}^{2} a^{2}+18 a c_{1} {\mathrm e}^{\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}+{\mathrm e}^{2 \operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}}{2} \\ y \left (x \right ) &= \frac {c_{1} x \left (81 c_{1}^{2} a^{2}+18 a c_{1} {\mathrm e}^{\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}+{\mathrm e}^{2 \operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}}{2} \\ y \left (x \right ) &= \frac {c_{1} x \left (81 c_{1}^{2} a^{2}+18 a c_{1} {\mathrm e}^{\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}+{\mathrm e}^{2 \operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x +6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x +2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}}{2} \\ y \left (x \right ) &= \frac {c_{1} x \left (81 c_{1}^{2} a^{2}+18 a c_{1} {\mathrm e}^{\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}+{\mathrm e}^{2 \operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x +54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x \,c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}}{2} \\ \end{align*} |
Problem 10118
| ODE |
\[ \boxed {\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime }=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -a \\ y \left (x \right ) &= a \\ y \left (x \right ) &= \frac {\left (x +\sqrt {-a^{2}+x^{2}}\right )^{c_{1}} c_{2}^{2}+\left (x +\sqrt {-a^{2}+x^{2}}\right )^{-c_{1}} a^{2}}{2 c_{2}} \\ \end{align*} |
Problem 10119
| ODE |
\[ \boxed {2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (y+1\right )=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10120
| ODE |
\[ \boxed {x^{3} y^{2} y^{\prime \prime }+\left (x +y\right ) \left (y^{\prime } x -y\right )^{3}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \operatorname {RootOf}\left (-2 \ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {i \sqrt {3}\, \operatorname {BesselY}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) c_{1} \sqrt {\textit {\_f}}+i \sqrt {3}\, \operatorname {BesselJ}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) \sqrt {\textit {\_f}}+\operatorname {BesselY}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) c_{1} \sqrt {\textit {\_f}}-2 c_{1} \operatorname {BesselY}\left (1+i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) \textit {\_f} +\operatorname {BesselJ}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) \sqrt {\textit {\_f}}-2 \operatorname {BesselJ}\left (1+i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) \textit {\_f}}{\textit {\_f}^{\frac {3}{2}} \left (\operatorname {BesselY}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right ) c_{1} +\operatorname {BesselJ}\left (i \sqrt {3}, 2 \sqrt {\textit {\_f}}\right )\right )}d \textit {\_f} \right )+2 c_{2} \right ) x \\ \end{align*} |
Problem 10121
| ODE |
\[ \boxed {y^{3} y^{\prime \prime }=a} \] |
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program solution |
\[ \frac {\sqrt {2 y^{2} c_{1} -a}}{2 c_{1}} = x +c_{2} \] Verified OK. \[ -\frac {\sqrt {2 y^{2} c_{1} -a}}{2 c_{1}} = c_{3} +x \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (\left (c_{2} +x \right )^{2} c_{1}^{2}+a \right ) c_{1}}}{c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {\left (\left (c_{2} +x \right )^{2} c_{1}^{2}+a \right ) c_{1}}}{c_{1}} \\ \end{align*} |
Problem 10122
| ODE |
\[ \boxed {y \left (y^{2}+1\right ) y^{\prime \prime }+\left (-3 y^{2}+1\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ y = -\frac {\sqrt {-2 c_{1} \left (x +c_{2} \right ) \left (2 c_{1} c_{2} +2 c_{1} x +1\right )}}{2 c_{1} \left (x +c_{2} \right )} \] Verified OK. \[ y = \frac {\sqrt {-2 c_{1} \left (x +c_{2} \right ) \left (2 c_{1} c_{2} +2 c_{1} x +1\right )}}{2 c_{1} \left (x +c_{2} \right )} \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= -i \\ y \left (x \right ) &= i \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {-2 \left (c_{1} x +c_{2} +\frac {1}{2}\right ) \left (c_{1} x +c_{2} \right )}}{2 c_{1} x +2 c_{2}} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {-2 \left (c_{1} x +c_{2} +\frac {1}{2}\right ) \left (c_{1} x +c_{2} \right )}}{2 c_{1} x +2 c_{2}} \\ \end{align*} |
Problem 10123
| ODE |
\[ \boxed {2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}=1} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10124
| ODE |
\[ \boxed {2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}=x^{2} a +b x +c} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10125
| ODE |
\[ \boxed {2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right )=0} \] |
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program solution |
\[ \text {Expression too large to display} \] Warning, solution could not be verified \[ \text {Expression too large to display} \] Warning, solution could not be verified |
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Maple solution | \begin{align*} \int _{}^{y \left (x \right )}\frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\sqrt {\left (a -\textit {\_m} \right ) \left (\left (\left (\left (a^{2}+4 a b +b^{2}\right ) A_{0} +B_{0} +C_{1} \right ) c^{2}+\left (4 a b \left (a +b \right ) A_{0} +4 C_{1} a +4 B_{0} b \right ) c +A_{0} a^{2} b^{2}+\left (B_{0} +D_{0} \right ) b^{2}+4 D_{0} a b +a^{2} \left (C_{1} +D_{0} \right )\right ) \left (\int \frac {\textit {\_m}^{2} {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (-2 A_{0} \left (a +b \right ) c^{2}+\left (\left (-2 a^{2}-8 a b -2 b^{2}\right ) A_{0} -2 B_{0} -2 C_{1} \right ) c -2 a b \left (a +b \right ) A_{0} +\left (-2 B_{0} -2 D_{0} \right ) b -2 a \left (C_{1} +D_{0} \right )\right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{3}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (c^{2} A_{0} +4 A_{0} \left (a +b \right ) c +\left (a^{2}+4 a b +b^{2}\right ) A_{0} +B_{0} +C_{1} +D_{0} \right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{4}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )-2 A_{0} \left (a +b +c \right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{5}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+A_{0} \left (\int \frac {\textit {\_m}^{6} {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (\left (-2 a b \left (a +b \right ) A_{0} -2 C_{1} a -2 B_{0} b \right ) c^{2}+\left (-2 A_{0} a^{2} b^{2}-2 B_{0} b^{2}-2 C_{1} a^{2}\right ) c -2 b D_{0} a \left (a +b \right )\right ) \left (\int \frac {\textit {\_m} \,{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (\left (A_{0} a^{2} b^{2}+B_{0} b^{2}+C_{1} a^{2}\right ) c^{2}+D_{0} a^{2} b^{2}\right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )-c_{1} \right ) {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}}d \textit {\_m} -x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\sqrt {\left (a -\textit {\_m} \right ) \left (\left (\left (\left (a^{2}+4 a b +b^{2}\right ) A_{0} +B_{0} +C_{1} \right ) c^{2}+\left (4 a b \left (a +b \right ) A_{0} +4 C_{1} a +4 B_{0} b \right ) c +A_{0} a^{2} b^{2}+\left (B_{0} +D_{0} \right ) b^{2}+4 D_{0} a b +a^{2} \left (C_{1} +D_{0} \right )\right ) \left (\int \frac {\textit {\_m}^{2} {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (-2 A_{0} \left (a +b \right ) c^{2}+\left (\left (-2 a^{2}-8 a b -2 b^{2}\right ) A_{0} -2 B_{0} -2 C_{1} \right ) c -2 a b \left (a +b \right ) A_{0} +\left (-2 B_{0} -2 D_{0} \right ) b -2 a \left (C_{1} +D_{0} \right )\right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{3}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (c^{2} A_{0} +4 A_{0} \left (a +b \right ) c +\left (a^{2}+4 a b +b^{2}\right ) A_{0} +B_{0} +C_{1} +D_{0} \right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{4}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )-2 A_{0} \left (a +b +c \right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}} \textit {\_m}^{5}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+A_{0} \left (\int \frac {\textit {\_m}^{6} {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (\left (-2 a b \left (a +b \right ) A_{0} -2 C_{1} a -2 B_{0} b \right ) c^{2}+\left (-2 A_{0} a^{2} b^{2}-2 B_{0} b^{2}-2 C_{1} a^{2}\right ) c -2 b D_{0} a \left (a +b \right )\right ) \left (\int \frac {\textit {\_m} \,{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )+\left (\left (A_{0} a^{2} b^{2}+B_{0} b^{2}+C_{1} a^{2}\right ) c^{2}+D_{0} a^{2} b^{2}\right ) \left (\int \frac {{\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}{\left (a -\textit {\_m} \right )^{2} \left (-\textit {\_m} +c \right ) \left (b -\textit {\_m} \right )}d \textit {\_m} \right )-c_{1} \right ) {\mathrm e}^{-\frac {\textit {\_m} \left (-2 a +\textit {\_m} \right )}{2}}}}d \textit {\_m} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10126
| ODE |
\[ \boxed {\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ \int _{}^{y}\frac {1}{c_{1} \sqrt {4 \textit {\_a}^{3}-\textit {\_a} a -b}}d \textit {\_a} = x +c_{2} \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= \frac {\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{6 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {-i \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}} \sqrt {3}+3 i \sqrt {3}\, a -\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}-3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {-i \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}} \sqrt {3}+3 i \sqrt {3}\, a +\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ \int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}-a \textit {\_a} -b}}d \textit {\_a} -c_{1} x -c_{2} &= 0 \\ \end{align*} |
Problem 10127
| ODE |
\[ \boxed {\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ \text {Expression too large to display} \] Warning, solution could not be verified |
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Maple solution | \begin{align*} y \left (x \right ) &= \frac {\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{6 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {-i \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}} \sqrt {3}+3 i \sqrt {3}\, a -\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}-3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {-i \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}} \sqrt {3}+3 i \sqrt {3}\, a +\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ c_{1} {\mathrm e}^{-f x}-c_{2} +\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}-a \textit {\_a} -b}}d \textit {\_a} &= 0 \\ \end{align*} |
Problem 10128
| ODE |
\[ \boxed {-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{\frac {3}{2}}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10129
| ODE |
\[ \boxed {2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10130
| ODE |
\[ \boxed {\left (y^{2}-1\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2}=0} \] |
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program solution |
\[ \frac {{\mathrm e}^{\frac {b \sqrt {1-y^{2}}\, \sqrt {1-a^{2} y^{2}}\, \operatorname {EllipticF}\left (y, a\right )}{\sqrt {a^{2} y^{4}-y^{2}-a^{2} y^{2}+1}}}}{c_{1} b} = x +c_{2} \] Verified OK.
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Maple solution | \[ \text {No solution found} \] |
Problem 10131
| ODE |
\[ \boxed {\left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+y d=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (a \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2}+1\right ) \left (-\textit {\_f}^{4} a c +\textit {\_f}^{4} b^{2}+\textit {\_f}^{2} a^{2} c_{1} -c \,\textit {\_f}^{2} a +b^{2} \textit {\_f}^{2}+a^{2} c_{1} +d \right )}}{-\textit {\_f}^{4} a c +\textit {\_f}^{4} b^{2}+\textit {\_f}^{2} a^{2} c_{1} -c \,\textit {\_f}^{2} a +b^{2} \textit {\_f}^{2}+a^{2} c_{1} +d}d \textit {\_f} \right ) \sqrt {a c -b^{2}}-a \arctan \left (\frac {a x +b}{\sqrt {a c -b^{2}}}\right )+c_{2} \sqrt {a c -b^{2}}\right ) \sqrt {a \,x^{2}+2 b x +c} \\ y \left (x \right ) &= \operatorname {RootOf}\left (-a \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2}+1\right ) \left (-\textit {\_f}^{4} a c +\textit {\_f}^{4} b^{2}+\textit {\_f}^{2} a^{2} c_{1} -c \,\textit {\_f}^{2} a +b^{2} \textit {\_f}^{2}+a^{2} c_{1} +d \right )}}{-\textit {\_f}^{4} a c +\textit {\_f}^{4} b^{2}+\textit {\_f}^{2} a^{2} c_{1} -c \,\textit {\_f}^{2} a +b^{2} \textit {\_f}^{2}+a^{2} c_{1} +d}d \textit {\_f} \right ) \sqrt {a c -b^{2}}-a \arctan \left (\frac {a x +b}{\sqrt {a c -b^{2}}}\right )+c_{2} \sqrt {a c -b^{2}}\right ) \sqrt {a \,x^{2}+2 b x +c} \\ \end{align*} |
Problem 10132
| ODE |
\[ \boxed {\sqrt {y}\, y^{\prime \prime }=a} \] |
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program solution |
\[ \frac {\frac {\left (4 \sqrt {y}\, a +2 c_{1} \right )^{\frac {3}{2}}}{3}-2 c_{1} \sqrt {4 \sqrt {y}\, a +2 c_{1}}}{4 a^{2}} = x +c_{2} \] Verified OK. \[ -\frac {\frac {\left (4 \sqrt {y}\, a +2 c_{1} \right )^{\frac {3}{2}}}{3}-2 c_{1} \sqrt {4 \sqrt {y}\, a +2 c_{1}}}{4 a^{2}} = c_{3} +x \] Verified OK.
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Maple solution |
\begin{align*} \frac {\left (-2 a \sqrt {y \left (x \right )}-c_{1} \right ) \sqrt {4 a \sqrt {y \left (x \right )}-c_{1}}-6 a^{2} \left (c_{2} +x \right )}{6 a^{2}} &= 0 \\ \frac {\left (2 a \sqrt {y \left (x \right )}+c_{1} \right ) \sqrt {4 a \sqrt {y \left (x \right )}-c_{1}}-6 a^{2} \left (c_{2} +x \right )}{6 a^{2}} &= 0 \\ \end{align*} |
Problem 10133
| ODE |
\[ \boxed {\sqrt {y^{2}+x^{2}}\, y^{\prime \prime }-a \left ({y^{\prime }}^{2}+1\right )^{\frac {3}{2}}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {-\operatorname {RootOf}\left (\arctan \left (\textit {\_g} \right )+\int _{}^{\textit {\_Z}}\frac {1+\sqrt {a^{2} \left (\textit {\_f}^{2}+1\right )}}{\left (\textit {\_f}^{2} a^{2}+a^{2}-1\right ) \left (\textit {\_f}^{2}+1\right )}d \textit {\_f} +c_{1} \right )+\textit {\_g}}{\textit {\_g}^{2}+1}d \textit {\_g} +c_{2} \right ) x \\ \end{align*} |
Problem 10134
| ODE |
\[ \boxed {y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ y = {\mathrm e}^{\frac {c_{1} c_{2} +c_{1} x -1}{c_{1} \left (x +c_{2} \right )}} \] Verified OK.
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Maple solution | \[ y \left (x \right ) = {\mathrm e}^{\frac {c_{1} x +c_{2} -1}{c_{1} x +c_{2}}} \] |
Problem 10135
| ODE |
\[ \boxed {\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right )=0} \] |
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program solution |
\[ \int _{}^{y}\frac {\sqrt {2}\, \left (b +a \sin \left (\textit {\_a} \right )^{2}\right )}{\sqrt {\left (b +a \sin \left (\textit {\_a} \right )^{2}\right ) \left (2 A a \sin \left (\textit {\_a} \right ) \cos \left (\textit {\_a} \right ) \textit {\_a} -A a \sin \left (\textit {\_a} \right )^{2}-A a \,\textit {\_a}^{2}-2 A \,\textit {\_a}^{2} c +4 c_{1} \right )}}d \textit {\_a} = x +c_{2} \] Verified OK. \[ \int _{}^{y}-\frac {\sqrt {2}\, \left (b +a \sin \left (\textit {\_a} \right )^{2}\right )}{\sqrt {\left (b +a \sin \left (\textit {\_a} \right )^{2}\right ) \left (2 A a \sin \left (\textit {\_a} \right ) \cos \left (\textit {\_a} \right ) \textit {\_a} -A a \sin \left (\textit {\_a} \right )^{2}-A a \,\textit {\_a}^{2}-2 A \,\textit {\_a}^{2} c +4 c_{1} \right )}}d \textit {\_a} = c_{3} +x \] Verified OK.
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Maple solution |
\begin{align*} \sqrt {2}\, \left (\int _{}^{y \left (x \right )}\frac {b +a \sin \left (\textit {\_a} \right )^{2}}{\sqrt {-\left (A a \sin \left (\textit {\_a} \right )^{2}-2 A a \textit {\_a} \cos \left (\textit {\_a} \right ) \sin \left (\textit {\_a} \right )+\textit {\_a}^{2} \left (a +2 c \right ) A -2 c_{1} \right ) \left (b +a \sin \left (\textit {\_a} \right )^{2}\right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ -\sqrt {2}\, \left (\int _{}^{y \left (x \right )}\frac {b +a \sin \left (\textit {\_a} \right )^{2}}{\sqrt {-\left (A a \sin \left (\textit {\_a} \right )^{2}-2 A a \textit {\_a} \cos \left (\textit {\_a} \right ) \sin \left (\textit {\_a} \right )+\textit {\_a}^{2} \left (a +2 c \right ) A -2 c_{1} \right ) \left (b +a \sin \left (\textit {\_a} \right )^{2}\right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10136
| ODE |
\[ \boxed {h \left (y\right ) y^{\prime \prime }+a D\left (h \right )\left (y\right ) {y^{\prime }}^{2}+j \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} \int _{}^{y \left (x \right )}\frac {h \left (\textit {\_b} \right )^{a}}{\sqrt {-2 \left (\int j \left (\textit {\_b} \right ) h \left (\textit {\_b} \right )^{-1+2 a}d \textit {\_b} \right )+c_{1}}}d \textit {\_b} -x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {h \left (\textit {\_b} \right )^{a}}{\sqrt {-2 \left (\int j \left (\textit {\_b} \right ) h \left (\textit {\_b} \right )^{-1+2 a}d \textit {\_b} \right )+c_{1}}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10137
| ODE |
\[ \boxed {h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right )=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10138
| ODE |
\[ \boxed {y^{\prime } y^{\prime \prime }-y x^{2} y^{\prime }-y^{2} x=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10139
| ODE |
\[ \boxed {\left (y^{\prime } x -y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= {\mathrm e}^{\int _{}^{\ln \left (x \right )}\left ({\mathrm e}^{\operatorname {RootOf}\left (\ln \left ({\mathrm e}^{\textit {\_Z}}-1\right ) {\mathrm e}^{\textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-\textit {\_b} \,{\mathrm e}^{\textit {\_Z}}+2\right )}-1\right )d \textit {\_b} +c_{2}} \\ \end{align*} |
Problem 10140
| ODE |
\[ \boxed {\left (y^{\prime } x -y\right ) y^{\prime \prime }-\left ({y^{\prime }}^{2}+1\right )^{2}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x \\ y \left (x \right ) &= i x \\ y \left (x \right ) &= \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {-\textit {\_f} +\operatorname {RootOf}\left (-c_{1} \tan \left (\frac {1}{\textit {\_Z}}\right ) \textit {\_Z} +\textit {\_f} c_{1} \tan \left (\frac {1}{\textit {\_Z}}\right )+c_{1} \textit {\_Z} \textit {\_f} +\tan \left (\frac {1}{\textit {\_Z}}\right ) \textit {\_Z} \textit {\_f} +c_{1} +\tan \left (\frac {1}{\textit {\_Z}}\right )+\textit {\_Z} -\textit {\_f} \right )}{\textit {\_f}^{2}+1}d \textit {\_f} +c_{2} \right ) x \\ \end{align*} |
Problem 10141
| ODE |
\[ \boxed {a \,x^{3} y^{\prime } y^{\prime \prime }+y^{2} b=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= {\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (-a \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\textit {\_a}^{3} a -a \,\textit {\_a}^{2}+b}d \textit {\_a} \right )-\textit {\_b} +c_{1} \right )d \textit {\_b} +c_{2}} \\ \end{align*} |
Problem 10142
| ODE |
\[ \boxed {\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10143
| ODE |
\[ \boxed {\left (2 y^{\prime } y^{2}+x^{2}\right ) y^{\prime \prime }+2 y {y^{\prime }}^{3}+3 y^{\prime } x +y=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10144
| ODE |
\[ \boxed {\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }+y^{3}=0} \] |
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program solution |
\[ \int _{}^{y}\frac {1}{\operatorname {RootOf}\left (2 \textit {\_Z}^{2}-\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-4 \sqrt {3}\, \ln \left (\textit {\_a} \right )-\sqrt {3}\, \ln \left (\frac {3}{4}+\frac {3 \tan \left (\textit {\_Z} \right )^{2}}{4}\right )+4 \sqrt {3}\, c_{2} -2 \textit {\_Z} \right )\right )+1\right ) \textit {\_a}}d \textit {\_a} = c_{3} +x \] Verified OK.
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\sqrt {c_{1} +\tan \left (\sqrt {3}\, x \right )}\, {\mathrm e}^{-\frac {\sqrt {3}\, \left (\int \frac {\sqrt {\left (9 c_{1}^{2}+12\right ) \sec \left (\sqrt {3}\, x \right )^{2}+3 c_{1}^{2}+6 c_{1} \tan \left (\sqrt {3}\, x \right )-3}}{c_{1} +\tan \left (\sqrt {3}\, x \right )}d x \right )}{6}+c_{2}}}{\left (\sec \left (\sqrt {3}\, x \right )^{2}\right )^{\frac {1}{4}}} \\ y \left (x \right ) &= \frac {\sqrt {c_{1} +\tan \left (\sqrt {3}\, x \right )}\, {\mathrm e}^{\frac {\sqrt {3}\, \left (\int \frac {\sqrt {\left (9 c_{1}^{2}+12\right ) \sec \left (\sqrt {3}\, x \right )^{2}+3 c_{1}^{2}+6 c_{1} \tan \left (\sqrt {3}\, x \right )-3}}{c_{1} +\tan \left (\sqrt {3}\, x \right )}d x \right )}{6}+c_{2}}}{\left (\sec \left (\sqrt {3}\, x \right )^{2}\right )^{\frac {1}{4}}} \\ \end{align*} |
Problem 10145
| ODE |
\[ \boxed {\left ({y^{\prime }}^{2}+a \left (y^{\prime } x -y\right )\right ) y^{\prime \prime }=b} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= -\frac {a \,x^{2}}{4}+\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1} \right ) \left (a \textit {\_f} +\sqrt {4 \textit {\_f} b -2 c_{1}}\right )}}{\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}}d \textit {\_f} +c_{2} \right ) \\ y \left (x \right ) &= -\frac {a \,x^{2}}{4}+\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1} \right ) \left (a \textit {\_f} -\sqrt {4 \textit {\_f} b -2 c_{1}}\right )}}{\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}}d \textit {\_f} +c_{2} \right ) \\ y \left (x \right ) &= -\frac {a \,x^{2}}{4}+\operatorname {RootOf}\left (-x -\left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1} \right ) \left (a \textit {\_f} +\sqrt {4 \textit {\_f} b -2 c_{1}}\right )}}{\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}}d \textit {\_f} \right )+c_{2} \right ) \\ y \left (x \right ) &= -\frac {a \,x^{2}}{4}+\operatorname {RootOf}\left (-x -\left (\int _{}^{\textit {\_Z}}\frac {\sqrt {\left (\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1} \right ) \left (a \textit {\_f} -\sqrt {4 \textit {\_f} b -2 c_{1}}\right )}}{\textit {\_f}^{2} a^{2}-4 \textit {\_f} b +2 c_{1}}d \textit {\_f} \right )+c_{2} \right ) \\ \end{align*} |
Problem 10146
| ODE |
\[ \boxed {\left (a \sqrt {{y^{\prime }}^{2}+1}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}=1} \] |
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program solution |
\[ y = \int \frac {c_{1} a +\sqrt {x^{2} a^{2}+c_{1}^{2} x^{2}-x^{4}}}{a^{2}-x^{2}}d x +c_{3} \] Verified OK. \[ y = \int -\frac {-c_{1} a +\sqrt {x^{2} a^{2}+c_{1}^{2} x^{2}-x^{4}}}{a^{2}-x^{2}}d x +c_{4} \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= -i x +c_{1} \\ y \left (x \right ) &= i x +c_{1} \\ y \left (x \right ) &= \frac {c_{2} a +\int \frac {-c_{1} a^{2}+x \sqrt {a^{2} \left (a^{2}+c_{1}^{2}-x^{2}\right )}}{a^{2}-x^{2}}d x}{a} \\ y \left (x \right ) &= \frac {c_{2} a -\left (\int \frac {c_{1} a^{2}+x \sqrt {a^{2} \left (a^{2}+c_{1}^{2}-x^{2}\right )}}{a^{2}-x^{2}}d x \right )}{a} \\ \end{align*} |
Problem 10147
| ODE |
\[ \boxed {h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }=-f} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10148
| ODE |
\[ \boxed {{y^{\prime \prime }}^{2}-a y=b} \] |
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program solution |
\[ \int _{}^{y}\frac {a \sqrt {6}}{2 \sqrt {a \left (2 \sqrt {\textit {\_a} a +b}\, a \textit {\_a} +2 \sqrt {\textit {\_a} a +b}\, b +3 c_{1} a \right )}}d \textit {\_a} = x +c_{2} \] Verified OK. \[ \int _{}^{y}-\frac {a \sqrt {6}}{2 \sqrt {a \left (2 \sqrt {\textit {\_a} a +b}\, a \textit {\_a} +2 \sqrt {\textit {\_a} a +b}\, b +3 c_{1} a \right )}}d \textit {\_a} = c_{3} +x \] Verified OK. \[ \int _{}^{y}\frac {3 a}{\sqrt {-6 a \left (2 \sqrt {\textit {\_a} a +b}\, a \textit {\_a} +2 \sqrt {\textit {\_a} a +b}\, b -3 c_{4} a \right )}}d \textit {\_a} = x +c_{5} \] Verified OK. \[ \int _{}^{y}-\frac {3 a}{\sqrt {-6 a \left (2 \sqrt {\textit {\_a} a +b}\, a \textit {\_a} +2 \sqrt {\textit {\_a} a +b}\, b -3 c_{4} a \right )}}d \textit {\_a} = x +c_{6} \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= -\frac {b}{a} \\ \sqrt {3}\, a \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {a \left (4 \textit {\_a} \sqrt {a \textit {\_a} +b}\, a +4 \sqrt {a \textit {\_a} +b}\, b -c_{1} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ -\sqrt {3}\, a \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {a \left (4 \textit {\_a} \sqrt {a \textit {\_a} +b}\, a +4 \sqrt {a \textit {\_a} +b}\, b -c_{1} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ -\sqrt {3}\, a \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-a \left (4 \textit {\_a} \sqrt {a \textit {\_a} +b}\, a +4 \sqrt {a \textit {\_a} +b}\, b -c_{1} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \sqrt {3}\, a \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-a \left (4 \textit {\_a} \sqrt {a \textit {\_a} +b}\, a +4 \sqrt {a \textit {\_a} +b}\, b -c_{1} \right )}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10149
| ODE |
\[ \boxed {a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime }=0} \] |
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program solution |
\[ y = c_{2} \] Verified OK. \[ y = \int \left (-\operatorname {RootOf}\left (2 a^{2} \textit {\_Z} \,\textit {\_Z}^{\frac {2 a}{2 a -1}}-4 x a \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+x \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+4 c_{1} a -c_{1} \right )^{2} a^{2}+2 \operatorname {RootOf}\left (2 a^{2} \textit {\_Z} \,\textit {\_Z}^{\frac {2 a}{2 a -1}}-4 x a \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+x \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+4 c_{1} a -c_{1} \right ) a x \right )d x +c_{3} \] Verified OK. \[ y = \int \left (-\operatorname {RootOf}\left (2 a^{2} \textit {\_Z} \,\textit {\_Z}^{\frac {2 a}{2 a -1}}-4 x a \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+x \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+4 c_{1} a -c_{1} \right )^{2} a^{2}+2 \operatorname {RootOf}\left (2 a^{2} \textit {\_Z} \,\textit {\_Z}^{\frac {2 a}{2 a -1}}-4 x a \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+x \,\textit {\_Z}^{\frac {2 a}{2 a -1}}+4 c_{1} a -c_{1} \right ) a x \right )d x +c_{4} \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= \int \operatorname {RootOf}\left (8 \textit {\_Z}^{1-2 a} a^{3} \sqrt {x^{2}-\textit {\_Z}}\, \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a}-8 \sqrt {x^{2}-\textit {\_Z}}\, \textit {\_Z}^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} a^{2} x^{2}+8 x \,\textit {\_Z}^{1-2 a} a^{3} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a}-8 \textit {\_Z}^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} a^{2} x^{3}+2 \sqrt {x^{2}-\textit {\_Z}}\, \textit {\_Z}^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} a \,x^{2}-4 x \,\textit {\_Z}^{1-2 a} a^{2} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a}+6 \textit {\_Z}^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} a \,x^{3}-\textit {\_Z}^{-2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} x^{3}-2 \sqrt {x^{2}-\textit {\_Z}}\, c_{1} a +2 c_{1} a x -c_{1} x \right )d x +c_{2} \\ y \left (x \right ) &= \int \operatorname {RootOf}\left (2 \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{2 a} \sqrt {x^{2}-\textit {\_Z}}\, \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \textit {\_Z}^{2 a} a +2 \left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \textit {\_Z}^{2 a} a x -\left (4 \textit {\_Z} \,a^{2}-4 a \,x^{2}+x^{2}\right )^{2 a} \left (x +\sqrt {x^{2}-\textit {\_Z}}\right )^{2 a} \left (-x +\sqrt {x^{2}-\textit {\_Z}}\right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}+2 a x -x \right )^{-2 a} \left (2 a \sqrt {x^{2}-\textit {\_Z}}-2 a x +x \right )^{2 a} \textit {\_Z}^{2 a} x -8 \sqrt {x^{2}-\textit {\_Z}}\, c_{1} \textit {\_Z} \,a^{3}+8 \sqrt {x^{2}-\textit {\_Z}}\, c_{1} a^{2} x^{2}+8 c_{1} \textit {\_Z} \,a^{3} x -8 c_{1} a^{2} x^{3}-2 \sqrt {x^{2}-\textit {\_Z}}\, c_{1} a \,x^{2}-4 c_{1} \textit {\_Z} \,a^{2} x +6 c_{1} a \,x^{3}-c_{1} x^{3}\right )d x +c_{2} \\ \end{align*} |
Problem 10150
| ODE |
\[ \boxed {2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= \frac {\left (c_{1} +\frac {\operatorname {arcsinh}\left (x \right )}{4}\right ) x \sqrt {x^{2}+1}}{2}-\frac {3 x^{2}}{16}+c_{1}^{2}+\frac {c_{1} \operatorname {arcsinh}\left (x \right )}{2}+\frac {\operatorname {arcsinh}\left (x \right )^{2}}{16} \\ y \left (x \right ) &= \frac {1}{2} c_{1} x^{2}+c_{2} x +c_{1}^{2}+c_{2}^{2} \\ \end{align*} |
Problem 10151
| ODE |
\[ \boxed {3 {y^{\prime \prime }}^{2} x^{2}-2 \left (3 y^{\prime } x +y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= x^{1+\frac {2 \sqrt {3}}{3}} c_{1} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {c_{1}^{2} x^{2}}{c_{2}}+c_{1} x +c_{2} \\ \end{align*} |
Problem 10152
| ODE |
\[ \boxed {x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (-6 x +1\right ) y^{\prime } y^{\prime \prime }+6 y^{\prime \prime } y-36 x {y^{\prime }}^{2}=0} \] |
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program solution |
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Maple solution | \begin{align*} y \left (x \right ) &= \frac {9 c_{1} \sqrt {\frac {-1+5 x +\sqrt {9 x^{2}-2 x}}{\sqrt {9 x^{2}-2 x}\, \sqrt {-\frac {\left (4 x -1\right )^{2}}{x \left (9 x -2\right )}}}}\, \sqrt {4 x -1}\, x}{\left (-1+9 x +3 \sqrt {9 x^{2}-2 x}\right ) \sqrt {27 x -3+9 \sqrt {9 x^{2}-2 x}}} \\ y \left (x \right ) &= \frac {c_{1} \left (-1+9 x +3 \sqrt {9 x^{2}-2 x}\right ) \sqrt {27 x -3+9 \sqrt {9 x^{2}-2 x}}\, \sqrt {4 x -1}\, x}{9 \sqrt {\frac {-1+5 x +\sqrt {9 x^{2}-2 x}}{\sqrt {9 x^{2}-2 x}\, \sqrt {-\frac {\left (4 x -1\right )^{2}}{x \left (9 x -2\right )}}}}} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} x^{3}+c_{2} x +\frac {c_{2}^{2}}{c_{1}} \\ \end{align*} |
Problem 10153
| ODE |
\[ \boxed {F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10154
| ODE |
\[ \boxed {y {y^{\prime \prime }}^{2}=a \,{\mathrm e}^{2 x}} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10155
| ODE |
\[ \boxed {\left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left ({y^{\prime }}^{2} a^{2}-1\right ) {y^{\prime }}^{2}=0} \] |
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program solution |
\[ y = \frac {c_{3} {\mathrm e}^{c_{1} x}-\sqrt {b^{2} c_{1}^{2}+1}}{c_{1} a} \] Verified OK. \[ \int _{}^{y}\frac {\sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b a}{a^{2} \textit {\_a}^{2}+\sqrt {-\frac {b^{2}}{a^{2} \textit {\_a}^{2}-b^{2}}}\, \sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b}d \textit {\_a} = x +c_{4} \] Verified OK. \[ \int _{}^{y}-\frac {\sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b a}{a^{2} \textit {\_a}^{2}-\sqrt {-\frac {b^{2}}{a^{2} \textit {\_a}^{2}-b^{2}}}\, \sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b}d \textit {\_a} = x +c_{5} \] Verified OK. \[ y = -\frac {c_{6} {\mathrm e}^{c_{2} x}-\sqrt {b^{2} c_{2}^{2}+1}}{c_{2} a} \] Verified OK. \[ \int _{}^{y}-\frac {\sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b a}{a^{2} \textit {\_a}^{2}+\sqrt {-\frac {b^{2}}{a^{2} \textit {\_a}^{2}-b^{2}}}\, \sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b}d \textit {\_a} = x +c_{7} \] Verified OK. \[ \int _{}^{y}\frac {\sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b a}{a^{2} \textit {\_a}^{2}-\sqrt {-\frac {b^{2}}{a^{2} \textit {\_a}^{2}-b^{2}}}\, \sqrt {-a^{2} \textit {\_a}^{2}+b^{2}}\, b}d \textit {\_a} = x +c_{8} \] Verified OK.
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Maple solution |
\begin{align*} y \left (x \right ) &= \frac {\operatorname {csgn}\left (\sec \left (\frac {c_{1} -x}{b}\right )\right ) \sin \left (\frac {c_{1} -x}{b}\right ) \operatorname {csgn}\left (a \right ) b}{a} \\ y \left (x \right ) &= -\frac {\operatorname {csgn}\left (\sec \left (\frac {c_{1} -x}{b}\right )\right ) \sin \left (\frac {c_{1} -x}{b}\right ) \operatorname {csgn}\left (a \right ) b}{a} \\ y \left (x \right ) &= -\frac {b}{a} \\ y \left (x \right ) &= \frac {b}{a} \\ y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {b \left ({\mathrm e}^{\frac {\sqrt {c_{1}^{2} a^{2}-1}\, \left (c_{2} +x \right )}{b}}-c_{1} \right )}{\sqrt {c_{1}^{2} a^{2}-1}} \\ \end{align*} |
Problem 10156
| ODE |
\[ \boxed {\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } y\right )^{2}-4 x y \left (y^{\prime } x -y\right )^{3}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10157
| ODE |
\[ \boxed {\left (2 y^{\prime \prime } y-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (y^{\prime \prime } x -y^{\prime }\right )^{3}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10158
| ODE |
\[ \boxed {\sqrt {a {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} b}+c y y^{\prime \prime }+d {y^{\prime }}^{2}=0} \] |
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program solution |
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Maple solution | \[ \text {No solution found} \] |
Problem 10159
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-a^{2} \left (\left (y^{\prime }\right )^{5}+2 \left (y^{\prime }\right )^{3}+y^{\prime }\right )=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= \int \operatorname {RootOf}\left (3 \left (\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {3 \textit {\_f}^{6} a^{2}+9 a^{2} \textit {\_f}^{4}+9 \textit {\_f}^{2} a^{2}+3 a^{2}+9 c_{1}}}d \textit {\_f} \right )+x +c_{2} \right )d x +c_{3} \\ y \left (x \right ) &= \int \operatorname {RootOf}\left (-3 \left (\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {3 \textit {\_f}^{6} a^{2}+9 a^{2} \textit {\_f}^{4}+9 \textit {\_f}^{2} a^{2}+3 a^{2}+9 c_{1}}}d \textit {\_f} \right )+x +c_{2} \right )d x +c_{3} \\ \end{align*} |
Problem 10160
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+1=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10161
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime } y+\left (y^{\prime }\right )^{2}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10162
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+a y y^{\prime \prime }=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10163
| ODE |
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10164
| ODE |
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime \prime }+x \left (y-1\right ) y^{\prime \prime }+x \left (y^{\prime }\right )^{2}+\left (1-y\right ) y^{\prime }=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \ln \left (x \right )+2 \left (\int _{}^{y \left (x \right )}\frac {1}{2 \operatorname {RootOf}\left (-2 \sqrt {4+c_{1}}\, \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} +2 \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} \textit {\_h} -4 \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) c_{2} +2 \operatorname {BesselY}\left (\frac {\sqrt {4+c_{1}}}{2}+1, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \sqrt {2}\, c_{2} \textit {\_Z} +2 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}+1, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \sqrt {2}\, \textit {\_Z} -2 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \sqrt {4+c_{1}}+2 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right ) \textit {\_h} -4 \operatorname {BesselJ}\left (\frac {\sqrt {4+c_{1}}}{2}, \frac {\sqrt {2}\, \textit {\_Z}}{2}\right )\right )^{2}+\textit {\_h}^{2}-c_{1} -4 \textit {\_h}}d \textit {\_h} \right )-c_{3} = 0 \] |
Problem 10165
| ODE |
Solve \begin {gather*} \boxed {y y^{\prime \prime \prime }-y^{\prime } y^{\prime \prime }+y^{3} y^{\prime }=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ -2 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\textit {\_a}^{4}+4 \textit {\_a}^{2} c_{2} -4 c_{2}^{2}+4 c_{1}}}d \textit {\_a} \right )-x -c_{3} &= 0 \\ 2 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\textit {\_a}^{4}+4 \textit {\_a}^{2} c_{2} -4 c_{2}^{2}+4 c_{1}}}d \textit {\_a} \right )-x -c_{3} &= 0 \\ \end{align*} |
Problem 10166
| ODE |
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime } y^{2}-18 y^{\prime } y^{\prime \prime } y+15 \left (y^{\prime }\right )^{3}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_h}^{2}+\sqrt {c_{1} \left (\textit {\_h}^{2}+c_{1} \right )}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ y \left (x \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (2 \left (\int _{}^{\textit {\_Z}}-\frac {1}{\textit {\_h}^{2}-\sqrt {c_{1} \left (\textit {\_h}^{2}+c_{1} \right )}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ \end{align*} |
Problem 10167
| ODE |
Solve \begin {gather*} \boxed {9 y^{\prime \prime \prime } y^{2}-45 y^{\prime } y^{\prime \prime } y+40 \left (y^{\prime }\right )^{3}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (-6 \left (\int _{}^{\textit {\_Z}}\frac {1}{4 \textit {\_h}^{2}+\sqrt {c_{1} \left (4 \textit {\_h}^{2}+c_{1} \right )}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ y \left (x \right ) &= {\mathrm e}^{\int \operatorname {RootOf}\left (6 \left (\int _{}^{\textit {\_Z}}-\frac {1}{4 \textit {\_h}^{2}-\sqrt {c_{1} \left (4 \textit {\_h}^{2}+c_{1} \right )}+c_{1}}d \textit {\_h} \right )+x +c_{2} \right )d x +c_{3}} \\ \end{align*} |
Problem 10168
| ODE |
Solve \begin {gather*} \boxed {2 y^{\prime } y^{\prime \prime \prime }-3 \left (y^{\prime }\right )^{2}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= c_{1} +c_{2} {\mathrm e}^{\frac {\sqrt {6}\, x}{2}}+c_{3} {\mathrm e}^{-\frac {\sqrt {6}\, x}{2}} \\ y \left (x \right ) &= c_{1} \\ \end{align*} |
Problem 10169
| ODE |
Solve \begin {gather*} \boxed {\left (\left (y^{\prime }\right )^{2}+1\right ) y^{\prime \prime \prime }-3 y^{\prime } \left (y^{\prime \prime }\right )^{2}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x +c_{1} \\ y \left (x \right ) &= i x +c_{1} \\ y \left (x \right ) &= -\sqrt {-c_{2}^{2}-2 c_{2} x -x^{2}+c_{1}}+c_{3} \\ y \left (x \right ) &= \sqrt {-c_{2}^{2}-2 c_{2} x -x^{2}+c_{1}}+c_{3} \\ \end{align*} |
Problem 10170
| ODE |
Solve \begin {gather*} \boxed {\left (\left (y^{\prime }\right )^{2}+1\right ) y^{\prime \prime \prime }-\left (3 y^{\prime }+a \right ) \left (y^{\prime \prime }\right )^{2}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= -i x +c_{1} \\ y \left (x \right ) &= i x +c_{1} \\ y \left (x \right ) &= \int \tan \left (\operatorname {RootOf}\left (c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} c_{2} a^{3}-2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} a^{3} x +\cos \left (\textit {\_Z} \right )^{2} c_{1}^{2} a^{2}+2 c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}-2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} c_{2} a -2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} a x -\sin \left (\textit {\_Z} \right )^{2} c_{1}^{2}+c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+x^{2} {\mathrm e}^{2 \textit {\_Z} a}\right )\right )d x +c_{3} \\ y \left (x \right ) &= \int \tan \left (\operatorname {RootOf}\left (c_{2}^{2} a^{4} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} a^{4} x \,{\mathrm e}^{2 \textit {\_Z} a}+a^{4} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} c_{2} a^{3}+2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} a^{3} x +\cos \left (\textit {\_Z} \right )^{2} c_{1}^{2} a^{2}+2 c_{2}^{2} a^{2} {\mathrm e}^{2 \textit {\_Z} a}+4 c_{2} a^{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+2 a^{2} x^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} c_{2} a +2 \cos \left (\textit {\_Z} \right ) {\mathrm e}^{\textit {\_Z} a} c_{1} a x -\sin \left (\textit {\_Z} \right )^{2} c_{1}^{2}+c_{2}^{2} {\mathrm e}^{2 \textit {\_Z} a}+2 c_{2} x \,{\mathrm e}^{2 \textit {\_Z} a}+x^{2} {\mathrm e}^{2 \textit {\_Z} a}\right )\right )d x +c_{3} \\ \end{align*} |
Problem 10171
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {\left (y^{\prime \prime }\right )^{2} b^{2}+1}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= -\frac {i x^{2}}{2 b}+c_{1} x +c_{2} \\ y \left (x \right ) &= \frac {i x^{2}}{2 b}+c_{1} x +c_{2} \\ y \left (x \right ) &= \frac {\int \left (-\ln \left (\frac {a^{2} b^{4} \left (c_{1} +x \right )+\sqrt {\left (-1+b^{2} \left (c_{1} +x \right ) a \right ) \left (1+b^{2} \left (c_{1} +x \right ) a \right )}\, \sqrt {a^{2} b^{4}}}{\sqrt {a^{2} b^{4}}}\right )+\left (c_{1} +x \right ) \sqrt {a^{2} b^{4}}\, \sqrt {\left (-1+b^{2} \left (c_{1} +x \right ) a \right ) \left (1+b^{2} \left (c_{1} +x \right ) a \right )}\right )d x +2 b \sqrt {a^{2} b^{4}}\, \left (c_{2} x +c_{3} \right )}{2 \sqrt {a^{2} b^{4}}\, b} \\ y \left (x \right ) &= -\frac {\int \left (-\ln \left (\frac {a^{2} b^{4} \left (c_{1} +x \right )+\sqrt {\left (-1+b^{2} \left (c_{1} +x \right ) a \right ) \left (1+b^{2} \left (c_{1} +x \right ) a \right )}\, \sqrt {a^{2} b^{4}}}{\sqrt {a^{2} b^{4}}}\right )+\left (c_{1} +x \right ) \sqrt {a^{2} b^{4}}\, \sqrt {\left (-1+b^{2} \left (c_{1} +x \right ) a \right ) \left (1+b^{2} \left (c_{1} +x \right ) a \right )}\right )d x -2 b \sqrt {a^{2} b^{4}}\, \left (c_{2} x +c_{3} \right )}{2 \sqrt {a^{2} b^{4}}\, b} \\ \end{align*} |
Problem 10172
| ODE |
Solve \begin {gather*} \boxed {y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+\left (y^{\prime }\right )^{3} y^{\prime \prime \prime }=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10173
| ODE |
Solve \begin {gather*} \boxed {y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+\left (y^{\prime }\right )^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+y^{\prime \prime } f \left (x \right )\right )+2 q \left (x \right ) \left (y^{\prime }\right )^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right )=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10174
| ODE |
Solve \begin {gather*} \boxed {3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 \left (y^{\prime \prime \prime }\right )^{2}=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= c_{1} x +c_{2} \\ y \left (x \right ) &= 3 \left (c_{2} +x \right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{c_{2} +x}}+c_{3} x +c_{4} \\ \end{align*} |
Problem 10175
| ODE |
Solve \begin {gather*} \boxed {9 \left (y^{\prime \prime }\right )^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \begin{align*} y \left (x \right ) &= c_{1} x +c_{2} \\ y \left (x \right ) &= \int \int \operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\operatorname {RootOf}\left (-20 \ln \left (\textit {\_f} \right )+\int _{}^{\textit {\_Z}}\textit {\_k} \left ({\mathrm e}^{\operatorname {RootOf}\left (81 \textit {\_k}^{2} {\mathrm e}^{\textit {\_Z}}+20 \,{\mathrm e}^{\textit {\_Z}} \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )-40 \,{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-20 \,{\mathrm e}^{\textit {\_Z}} \ln \left (5\right )+162 c_{1} {\mathrm e}^{\textit {\_Z}}-20 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+2187 \textit {\_k}^{2}+540 \ln \left ({\mathrm e}^{\textit {\_Z}}+27\right )-1080 \ln \left (2\right )-540 \ln \left (5\right )+4374 c_{1} -540 \textit {\_Z} -540\right )}+27\right )d \textit {\_k} +20 c_{2} \right )}d \textit {\_f} \right )+x +c_{3} \right )d x d x +c_{4} x +c_{5} \\ \end{align*} |
Problem 10176
| ODE |
\[ \boxed {y^{\prime \prime }-f \left (y\right )=0} \] |
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program solution |
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Maple solution | \begin{align*} \int _{}^{y \left (x \right )}\frac {1}{\sqrt {2 \left (\int f \left (\textit {\_b} \right )d \textit {\_b} \right )+c_{1}}}d \textit {\_b} -x -c_{2} &= 0 \\ -\left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {2 \left (\int f \left (\textit {\_b} \right )d \textit {\_b} \right )+c_{1}}}d \textit {\_b} \right )-x -c_{2} &= 0 \\ \end{align*} |
Problem 10177
| ODE |
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-f \left (y\right )=0} \end {gather*} |
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program solution |
N/A |
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Maple solution | \[ \text {No solution found} \] |
Problem 10178
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a x \left (t \right )\\ y^{\prime }\left (t \right )&=b \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{a t} \\ y \left (t \right ) &= b t +c_{2} \\ \end{align*} |
Problem 10179
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a y \left (t \right )\\ y^{\prime }\left (t \right )&=-a x \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (a t \right )+c_{2} \cos \left (a t \right ) \\ y \left (t \right ) &= \cos \left (a t \right ) c_{1} -\sin \left (a t \right ) c_{2} \\ \end{align*} |
Problem 10180
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a y \left (t \right )\\ y^{\prime }\left (t \right )&=b x \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}+c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t} \\ y \left (t \right ) &= \frac {\sqrt {b}\, \left (c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}-c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t}\right )}{\sqrt {a}} \\ \end{align*} |
Problem 10181
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+a y \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{a t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{a t} \left (c_{2} \sin \left (t \right )-c_{1} \cos \left (t \right )\right ) \\ \end{align*} |
Problem 10182
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a x \left (t \right )+b y \left (t \right )\\ y^{\prime }\left (t \right )&=c x \left (t \right )+b y \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\frac {\left (a +b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (-a -b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}} \\ y \left (t \right ) &= \left (\frac {1}{2}+\frac {\frac {\sqrt {a^{2}-2 a b +b^{2}+4 b c}}{2}-\frac {a}{2}}{b}\right ) c_{1} {\mathrm e}^{\frac {\left (a +b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}}+\left (\frac {{\mathrm e}^{-\frac {\left (-a -b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}}}{2}+\frac {-\frac {\sqrt {a^{2}-2 a b +b^{2}+4 b c}\, {\mathrm e}^{-\frac {\left (-a -b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}}}{2}-\frac {{\mathrm e}^{-\frac {\left (-a -b +\sqrt {a^{2}-2 a b +b^{2}+4 b c}\right ) t}{2}} a}{2}}{b}\right ) c_{2} \\ \end{align*} |
Problem 10183
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=\frac {x \left (t \right ) a \alpha }{a^{2}+b^{2}}+\frac {x \left (t \right ) b \beta }{a^{2}+b^{2}}+\frac {y \left (t \right ) a \beta }{a^{2}+b^{2}}-\frac {y \left (t \right ) \alpha b}{a^{2}+b^{2}}\\ y^{\prime }\left (t \right )&=-\frac {\beta x \left (t \right ) a}{a^{2}+b^{2}}+\frac {x \left (t \right ) \alpha b}{a^{2}+b^{2}}+\frac {\alpha y \left (t \right ) a}{a^{2}+b^{2}}+\frac {y \left (t \right ) b \beta }{a^{2}+b^{2}} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\frac {\left (i a \beta -i \alpha b +a \alpha +b \beta \right ) t}{a^{2}+b^{2}}}+c_{2} {\mathrm e}^{-\frac {\left (i a \beta -i \alpha b -a \alpha -b \beta \right ) t}{a^{2}+b^{2}}} \\ y \left (t \right ) &= i \left (c_{1} {\mathrm e}^{\frac {\left (i a \beta -i \alpha b +a \alpha +b \beta \right ) t}{a^{2}+b^{2}}}-c_{2} {\mathrm e}^{-\frac {\left (i a \beta -i \alpha b -a \alpha -b \beta \right ) t}{a^{2}+b^{2}}}\right ) \\ \end{align*} |
Problem 10184
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+2 y \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= -{\mathrm e}^{t} \left (c_{1} \sin \left (t \right )-c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ \end{align*} |
Problem 10185
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )-5 y \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-7 t}+c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{-7 t}-\frac {c_{2} {\mathrm e}^{-t}}{2} \\ \end{align*} |
Problem 10186
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-7 y \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-6 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{-6 t} \left (c_{1} \sin \left (t \right )+c_{2} \sin \left (t \right )-c_{1} \cos \left (t \right )+c_{2} \cos \left (t \right )\right )}{2} \\ \end{align*} |
Problem 10187
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}\\ y^{\prime }\left (t \right )&=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\left (\frac {a_{1}}{2}+\frac {b_{2}}{2}+\frac {\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}}{2}\right ) t} c_{4} +{\mathrm e}^{\left (\frac {a_{1}}{2}+\frac {b_{2}}{2}-\frac {\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}}{2}\right ) t} c_{3} +\frac {b_{1} c_{2} -b_{2} c_{1}}{a_{1} b_{2} -a_{2} b_{1}} \\ y \left (t \right ) &= \frac {-\frac {a_{1} \left ({\mathrm e}^{\frac {\left (a_{1} +b_{2} +\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) t}{2}} c_{4} \left (a_{1} b_{2} -a_{2} b_{1} \right )+{\mathrm e}^{\frac {\left (a_{1} +b_{2} -\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) t}{2}} c_{3} \left (a_{1} b_{2} -a_{2} b_{1} \right )-b_{2} c_{1} +b_{1} c_{2} \right ) \left (2 a_{1} b_{2} -2 a_{2} b_{1} \right )}{a_{1} b_{2} -a_{2} b_{1}}+\frac {\left (a_{1} +b_{2} +\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) {\mathrm e}^{\frac {\left (a_{1} +b_{2} +\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) t}{2}} c_{4} \left (2 a_{1} b_{2} -2 a_{2} b_{1} \right )}{2}+\frac {\left (a_{1} +b_{2} -\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) {\mathrm e}^{\frac {\left (a_{1} +b_{2} -\sqrt {a_{1}^{2}-2 a_{1} b_{2} +4 a_{2} b_{1} +b_{2}^{2}}\right ) t}{2}} c_{3} \left (2 a_{1} b_{2} -2 a_{2} b_{1} \right )}{2}-c_{1} \left (2 a_{1} b_{2} -2 a_{2} b_{1} \right )}{\left (2 a_{1} b_{2} -2 a_{2} b_{1} \right ) b_{1}} \\ \end{align*} |
Problem 10188
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-2 y \left (t \right )+3 t\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+4 \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )-\frac {5}{4} \\ y \left (t \right ) &= -c_{2} \cos \left (2 t \right )+c_{1} \sin \left (2 t \right )+\frac {3 t}{2} \\ \end{align*} |
Problem 10189
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=t^{2}-y \left (t \right )-6 t -1\\ y^{\prime }\left (t \right )&=-3 t^{2}+x \left (t \right )+3 t +1 \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+3 t^{2}-t -13 \\ y \left (t \right ) &= t^{2}-c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )-12 t \\ \end{align*} |
Problem 10190
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=-x \left (t \right )-5 y \left (t \right )+{\mathrm e}^{t} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} t c_{1} +\frac {{\mathrm e}^{t}}{25}+\frac {7 \,{\mathrm e}^{2 t}}{36} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{36}-c_{2} {\mathrm e}^{-4 t}-{\mathrm e}^{-4 t} t c_{1} +{\mathrm e}^{-4 t} c_{1} +\frac {4 \,{\mathrm e}^{t}}{25} \\ \end{align*} |
Problem 10191
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ODE |
\begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right )+{\mathrm e}^{2 t}+t\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{t}-1 \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= \frac {3 t}{7}-\frac {1}{49}-\frac {{\mathrm e}^{t}}{6}+\frac {5 \,{\mathrm e}^{2 t}}{17}+{\mathrm e}^{-\frac {7 t}{5}} c_{1} \\ y \left (t \right ) &= -\frac {{\mathrm e}^{2 t}}{17}+\frac {t}{7}-\frac {26}{49}+\frac {{\mathrm e}^{t}}{4}+\frac {3 \,{\mathrm e}^{-\frac {7 t}{5}} c_{1}}{2} \\ \end{align*} |
Problem 10192
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-3 y \left (t \right )-{\mathrm e}^{t}+\cos \left (t \right )\\ y^{\prime }\left (t \right )&=4 y \left (t \right )+2 \,{\mathrm e}^{t}-\cos \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= \frac {c_{1} {\mathrm e}^{4 t}}{4}+\frac {5 \sin \left (t \right )}{17}+{\mathrm e}^{t}-\frac {3 \cos \left (t \right )}{17}+c_{2} \\ y \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{4 t}}{3}+\frac {4 \cos \left (t \right )}{17}-\frac {2 \,{\mathrm e}^{t}}{3}-\frac {\sin \left (t \right )}{17} \\ \end{align*} |
Problem 10193
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-27-5 x \left (t \right )-y \left (t \right )+7 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=12+2 x \left (t \right )-3 y \left (t \right )-3 \,{\mathrm e}^{t} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} +{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} -\frac {93}{17}+\frac {31 \,{\mathrm e}^{t}}{26} \\ y \left (t \right ) &= -{\mathrm e}^{-4 t} \sin \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{2} -{\mathrm e}^{-4 t} \cos \left (t \right ) c_{1} +{\mathrm e}^{-4 t} \sin \left (t \right ) c_{1} -\frac {2 \,{\mathrm e}^{t}}{13}+\frac {6}{17} \\ \end{align*} |
Problem 10194
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-y \left (t \right )+7 \,{\mathrm e}^{t}-9 \,{\mathrm e}^{2 t}\\ y^{\prime }\left (t \right )&=x \left (t \right )-3 y \left (t \right )-3 \,{\mathrm e}^{t}+4 \,{\mathrm e}^{2 t} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} t c_{1} +\frac {31 \,{\mathrm e}^{t}}{25}-\frac {49 \,{\mathrm e}^{2 t}}{36} \\ y \left (t \right ) &= \frac {19 \,{\mathrm e}^{2 t}}{36}-c_{2} {\mathrm e}^{-4 t}-{\mathrm e}^{-4 t} t c_{1} -{\mathrm e}^{-4 t} c_{1} -\frac {11 \,{\mathrm e}^{t}}{25} \\ \end{align*} |
Problem 10195
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right )+7 t -9 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )-5 y \left (t \right )-3 t +4 \,{\mathrm e}^{t} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-t}+{\mathrm e}^{-6 t} c_{1} -\frac {29 \,{\mathrm e}^{t}}{7}+\frac {19 t}{3}-\frac {56}{9} \\ y \left (t \right ) &= -c_{2} {\mathrm e}^{-t}+4 \,{\mathrm e}^{-6 t} c_{1} +\frac {24 \,{\mathrm e}^{t}}{7}+\frac {55}{9}-\frac {17 t}{3} \\ \end{align*} |
Problem 10196
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) g \left (t \right )+y \left (t \right ) f \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\int \left (\tan \left (c_{1} -\left (\int g \left (t \right )d t \right )\right ) g \left (t \right )+f \left (t \right )\right )d t} c_{2} \\ y \left (t \right ) &= {\mathrm e}^{\int \left (\tan \left (c_{1} -\left (\int g \left (t \right )d t \right )\right ) g \left (t \right )+f \left (t \right )\right )d t} c_{2} \tan \left (c_{1} -\left (\int g \left (t \right )d t \right )\right ) \\ \end{align*} |
Problem 10197
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right ) f \left (t \right ) a -y \left (t \right ) f \left (t \right ) b +g \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) f \left (t \right ) c -f \left (t \right ) y \left (t \right ) d +h \left (t \right ) \end {align*}
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program solution |
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Maple solution |
\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*} |
Problem 10198
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=x \left (t \right ) \cos \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{\sin \left (t \right )} \\ y \left (t \right ) &= c_{2} t +c_{1} \\ \end{align*} |
Problem 10199
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-\frac {y \left (t \right )}{t}\\ y^{\prime }\left (t \right )&=-\frac {x \left (t \right )}{t} \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= \frac {c_{1} t^{2}+c_{2}}{t} \\ y \left (t \right ) &= -\frac {c_{1} t^{2}-c_{2}}{t} \\ \end{align*} |
Problem 10200
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ODE |
\begin {align*} x^{\prime }\left (t \right )&=-\frac {2 x \left (t \right )}{t}+1\\ y^{\prime }\left (t \right )&=y \left (t \right )+x \left (t \right )+\frac {2 x \left (t \right )}{t}-1 \end {align*}
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program solution |
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Maple solution |
\begin{align*} x \left (t \right ) &= \frac {t}{3}+\frac {c_{2}}{t^{2}} \\ y \left (t \right ) &= \frac {3 c_{1} {\mathrm e}^{t} t^{2}-t^{3}-3 c_{2}}{3 t^{2}} \\ \end{align*} |