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ODE |
Mathematica |
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\[
{}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\] |
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\[
{}y^{\prime \prime }+y y^{\prime }-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0
\] |
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\[
{}y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\left (x \right )}{2 f \left (x \right )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\left (x \right ) y^{2}}{2 f \left (x \right )}+\frac {\left (f \left (x \right )+\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-f^{\prime \prime }\left (x \right )\right ) y}{2 f \left (x \right )} = 0
\] |
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\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0
\] |
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\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\] |
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\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0
\] |
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\[
{}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\] |
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\[
{}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0
\] |
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\[
{}y^{\prime \prime }-f \left (y^{\prime }, a x +b y\right ) = 0
\] |
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\[
{}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0
\] |
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\[
{}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{1-n}\right ) = 0
\] |
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\[
{}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\] |
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\[
{}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\] |
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\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\] |
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\[
{}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\] |
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\[
{}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right ) = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\] |
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\[
{}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\] |
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\[
{}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\] |
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\[
{}y^{\prime \prime } \sqrt {x}-y^{{3}/{2}} = 0
\] |
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\[
{}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}} = 0
\] |
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\[
{}f \left (x \right )^{2} y^{\prime \prime }+f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }-h \left (y, f \left (x \right ) y^{\prime }\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-a x = 0
\] |
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\[
{}y y^{\prime \prime }-a \,x^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime }+f \left (x \right ) y^{3}+y^{2} \left (\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 y^{2} a +b y^{3} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (y^{2} b^{2}-a^{2}\right ) = 0
\] |
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\[
{}y y^{\prime \prime }+a {y^{\prime }}^{2}+f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+3 f \left (x \right ) y y^{\prime }+2 \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y^{2}-8 y^{3} = 0
\] |
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\[
{}2 y y^{\prime \prime }-{y^{\prime }}^{2}+4 y^{\prime } y^{2}+1+y^{2} f \left (x \right )+y^{4} = 0
\] |
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\[
{}2 y y^{\prime \prime }-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0
\] |
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\[
{}4 y y^{\prime \prime }-3 {y^{\prime }}^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\left (x \right ) y}{f \left (x \right )}\right ) y^{\prime }+y^{4}-2 y^{\prime } y^{2}+g \left (x \right ) y^{2}+f \left (x \right ) y = 0
\] |
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\[
{}a y y^{\prime \prime }-\left (a -1\right ) {y^{\prime }}^{2}+\left (2+a \right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3} = 0
\] |
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\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\] |
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\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\] |
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\[
{}\operatorname {f0} \left (x \right ) y y^{\prime \prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f3} \left (x \right ) y^{2} = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\] |
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\[
{}2 y \left (y-1\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (y-1\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
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\[
{}-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
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\[
{}2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (y^{2} a +b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\] |
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\[
{}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\] |
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\[
{}2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
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\[
{}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{{3}/{2}} = 0
\] |
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\[
{}2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2} = 0
\] |
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\[
{}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
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\[
{}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0
\] |
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\[
{}y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\] |
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\[
{}\left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
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\[
{}a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\] |
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\[
{}\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2} = 0
\] |
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\[
{}\left (x^{2}+2 y^{\prime } y^{2}\right ) y^{\prime \prime }+2 {y^{\prime }}^{3} y+3 x y^{\prime }+y = 0
\] |
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\[
{}h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }+f = 0
\] |
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\[
{}a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\] |
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\[
{}F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2} = 0
\] |
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\[
{}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\] |
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\[
{}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime \prime }+a y y^{\prime \prime } = 0
\] |
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\[
{}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 x y-1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0
\] |
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\[
{}y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0
\] |
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\[
{}y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right ) = 0
\] |
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\[
{}y^{\prime \prime \prime } = f \left (y\right )
\] |
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\[
{}\left [x^{\prime \prime }\left (t \right ) = \left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x \left (t \right )+\frac {3 c^{2} y \left (t \right ) \sin \left (2 a t b \right )}{2}, y^{\prime \prime }\left (t \right ) = \left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y \left (t \right )+\frac {3 c^{2} x \left (t \right ) \sin \left (2 a t b \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = h \left (t \right ) y \left (t \right )-g \left (t \right ) z \left (t \right ), y^{\prime }\left (t \right ) = f \left (t \right ) z \left (t \right )-h \left (t \right ) x \left (t \right ), z^{\prime }\left (t \right ) = g \left (t \right ) x \left (t \right )-f \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) \left (a \left (p x \left (t \right )+q y \left (t \right )\right )+\alpha \right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\beta +b \left (p x \left (t \right )+q y \left (t \right )\right )\right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right ) y \left (t \right )^{2}+x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )^{2} y \left (t \right )-x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\] |
✗ |
✗ |
|