2.17.74 Problems 7301 to 7400

Problem 7301

ODE	\[ \boxed {y^{\prime }+y=\frac {1}{x^{2}}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7302

ODE	\[ \boxed {x y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = c_{1} \left (\frac {1}{x}+O\left (x^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{1}}{x}+O\left (x^{6}\right ) \]

Problem 7303

ODE	\[ \boxed {y^{\prime }=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7304

ODE	\[ \boxed {y^{\prime \prime }=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7305

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime }=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7306

ODE	\[ \boxed {y^{\prime \prime }+y=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7307

ODE	\[ \boxed {y^{\prime \prime }+y^{\prime }+y=\frac {1}{x}} \] With the expansion point for the power series method at \(x = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 7308

ODE	\[ \boxed {h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}=b^{2}} \]
program solution	\[ \int _{}^{h}-\frac {\left (\textit {\_a} +b \right ) \left (\textit {\_a} -b \right )}{\sqrt {-\textit {\_a}^{4}+4 \textit {\_a}^{2} a^{2}+2 \textit {\_a}^{2} b^{2}-b^{4}}}d \textit {\_a} = u +c_{1} \] Verified OK. \[ \int _{}^{h}\frac {\left (\textit {\_a} +b \right ) \left (\textit {\_a} -b \right )}{\sqrt {-\textit {\_a}^{4}+4 \textit {\_a}^{2} a^{2}+2 \textit {\_a}^{2} b^{2}-b^{4}}}d \textit {\_a} = u +c_{2} \] Verified OK.
Maple solution	\begin{align*} u -\left (\int _{}^{h \left (u \right )}\frac {\textit {\_a}^{2}-b^{2}}{\sqrt {-\textit {\_a}^{4}+\left (4 a^{2}+2 b^{2}\right ) \textit {\_a}^{2}-b^{4}}}d \textit {\_a} \right )-c_{1} &= 0 \\ u +\int _{}^{h \left (u \right )}\frac {\textit {\_a}^{2}-b^{2}}{\sqrt {-\textit {\_a}^{4}+\left (4 a^{2}+2 b^{2}\right ) \textit {\_a}^{2}-b^{4}}}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

Problem 7309

ODE	\[ \boxed {y^{\prime \prime }+2 y^{\prime }-24 y=16-\left (x +2\right ) {\mathrm e}^{4 x}} \]
program solution	\[ y = c_{1} {\mathrm e}^{-6 x}+\frac {c_{2} {\mathrm e}^{4 x}}{10}-\frac {2}{3}+\frac {\left (-50 x^{2}-190 x +19\right ) {\mathrm e}^{4 x}}{1000} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (\left (x^{2}+\frac {19}{5} x -20 c_{2} -\frac {19}{50}\right ) {\mathrm e}^{10 x}-20 c_{1} +\frac {40 \,{\mathrm e}^{6 x}}{3}\right ) {\mathrm e}^{-6 x}}{20} \]

Problem 7310

ODE	\[ \boxed {y^{\prime \prime }+3 y^{\prime }-4 y=6 \,{\mathrm e}^{2 t -2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 4, y^{\prime }\left (1\right ) = 5] \end {align*}
program solution	\[ y = {\mathrm e}^{2 t -2}+3 \,{\mathrm e}^{t -1} \] Verified OK.
Maple solution	\[ y \left (t \right ) = {\mathrm e}^{2 t -2}+3 \,{\mathrm e}^{t -1} \]

Problem 7311

ODE	\[ \boxed {y^{\prime \prime }+y={\mathrm e}^{a \cos \left (x \right )}} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (\frac {1}{40320} x^{8}-\frac {1}{720} x^{6}+\frac {1}{24} x^{4}+1-\frac {1}{2} x^{2}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}+\frac {1}{120} x^{5}-\frac {1}{5040} x^{7}\right ) y^{\prime }\left (0\right )+\frac {x^{2} {\mathrm e}^{a}}{2}-\frac {x^{4} {\mathrm e}^{a} a}{24}-\frac {x^{4} {\mathrm e}^{a}}{24}+\frac {x^{6} {\mathrm e}^{a} a^{2}}{240}+\frac {x^{6} {\mathrm e}^{a} a}{360}+\frac {x^{6} {\mathrm e}^{a}}{720}-\frac {x^{8} {\mathrm e}^{a} a^{3}}{2688}-\frac {x^{8} {\mathrm e}^{a} a^{2}}{2240}-\frac {x^{8} {\mathrm e}^{a} a}{13440}-\frac {x^{8} {\mathrm e}^{a}}{40320}+O\left (x^{8}\right ) \] Verified OK. \[ y = \left (-\frac {1}{720} x^{6}+\frac {1}{24} x^{4}+1-\frac {1}{2} x^{2}\right ) c_{1} +\left (x -\frac {1}{6} x^{3}+\frac {1}{120} x^{5}-\frac {1}{5040} x^{7}\right ) c_{2} +\frac {x^{2} {\mathrm e}^{a}}{2}+\left (-\frac {{\mathrm e}^{a} a}{24}-\frac {{\mathrm e}^{a}}{24}\right ) x^{4}+\left (\frac {{\mathrm e}^{a} a}{360}+\frac {{\mathrm e}^{a} a^{2}}{240}+\frac {{\mathrm e}^{a}}{720}\right ) x^{6}+O\left (x^{8}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{24} x^{4}-\frac {1}{720} x^{6}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}+\frac {1}{120} x^{5}-\frac {1}{5040} x^{7}\right ) D\left (y \right )\left (0\right )+\frac {{\mathrm e}^{a} x^{2}}{2}+\frac {\left (-a -1\right ) {\mathrm e}^{a} x^{4}}{24}+\frac {\left (3 a^{2}+2 a +1\right ) {\mathrm e}^{a} x^{6}}{720}+O\left (x^{8}\right ) \]

Problem 7312

ODE	\[ \boxed {y^{\prime }-\frac {y}{2 y \ln \left (y\right )+y-x}=0} \]
program solution	\[ y^{2} \ln \left (y\right )-y x = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-x \,{\mathrm e}^{\textit {\_Z}}+c_{1} \right )} \]

Problem 7313

ODE	\[ \boxed {x y^{\prime \prime }-\left (1+2 x \right ) y^{\prime }+\left (1+x \right ) y=0} \]
program solution	\[ y = {\mathrm e}^{x} c_{1} +\frac {c_{2} {\mathrm e}^{x} x^{2}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{2} x^{2}+c_{1} \right ) \]

Problem 7314

ODE	\[ \boxed {y^{\prime } x^{2}+{\mathrm e}^{-y}=0} \]
program solution	\[ y = \ln \left (-\frac {c_{1} x -1}{x}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \ln \left (\frac {-c_{1} x +1}{x}\right ) \]

Problem 7315

ODE	\[ \boxed {y^{\prime \prime }+{\mathrm e}^{y}=0} \]
program solution	\[ y = \ln \left (-\tanh \left (\frac {\sqrt {c_{1}}\, \left (x +c_{2} \right ) \sqrt {2}}{2}\right )^{2} c_{1} +c_{1} \right ) \] Verified OK. \[ y = \ln \left (-\tanh \left (\frac {\sqrt {c_{1}}\, \left (x +c_{3} \right ) \sqrt {2}}{2}\right )^{2} c_{1} +c_{1} \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\ln \left (2\right )+\ln \left (\frac {\operatorname {sech}\left (\frac {x +c_{2}}{2 c_{1}}\right )^{2}}{c_{1}^{2}}\right ) \]

Problem 7316

ODE	\[ \boxed {y^{\prime }-\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6}=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 7317

ODE	\[ \boxed {y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7318

ODE	\[ \boxed {y^{\prime }=a} \]
program solution	\[ y = a x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = a x +c_{1} \]

Problem 7319

ODE	\[ \boxed {y^{\prime }=x} \]
program solution	\[ y = \frac {x^{2}}{2}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2}}{2}+c_{1} \]

Problem 7320

ODE	\[ \boxed {y^{\prime }=1} \]
program solution	\[ y = x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x +c_{1} \]

Problem 7321

ODE	\[ \boxed {y^{\prime }=a x} \]
program solution	\[ y = \frac {a \,x^{2}}{2}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {a \,x^{2}}{2}+c_{1} \]

Problem 7322

ODE	\[ \boxed {y^{\prime }-a x y=0} \]
program solution	\[ y = {\mathrm e}^{\frac {1}{2} a \,x^{2}+c_{1} a} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {a \,x^{2}}{2}} \]

Problem 7323

ODE	\[ \boxed {y^{\prime }-y=a x} \]
program solution	\[ y = -\left (a x \,{\mathrm e}^{-x}+a \,{\mathrm e}^{-x}-c_{1} \right ) {\mathrm e}^{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{x}-a \left (x +1\right ) \]

Problem 7324

ODE	\[ \boxed {y^{\prime }-b y=a x} \]
program solution	\[ y = -\frac {\left (a x b \,{\mathrm e}^{-x b}-c_{1} b^{2}+a \,{\mathrm e}^{-x b}\right ) {\mathrm e}^{x b}}{b^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{b x} c_{1} b^{2}-a x b -a}{b^{2}} \]

Problem 7325

ODE	\[ \boxed {y^{\prime }-y=0} \]
program solution	\[ y = {\mathrm e}^{x} c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} {\mathrm e}^{x} \]

Problem 7326

ODE	\[ \boxed {y^{\prime }-b y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x b} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{b x} c_{1} \]

Problem 7327

ODE	\[ \boxed {y^{\prime }-b y^{2}=a x} \]
program solution	\[ y = \frac {\left (\operatorname {AiryAi}\left (1, -\left (a b \right )^{\frac {1}{3}} x \right ) c_{3} +\operatorname {AiryBi}\left (1, -\left (a b \right )^{\frac {1}{3}} x \right )\right ) \left (a b \right )^{\frac {1}{3}}}{b \left (c_{3} \operatorname {AiryAi}\left (-\left (a b \right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (a b \right )^{\frac {1}{3}} x \right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (a b \right )^{\frac {1}{3}} \left (\operatorname {AiryAi}\left (1, -\left (a b \right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (1, -\left (a b \right )^{\frac {1}{3}} x \right )\right )}{b \left (c_{1} \operatorname {AiryAi}\left (-\left (a b \right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (a b \right )^{\frac {1}{3}} x \right )\right )} \]

Problem 7328

ODE	\[ \boxed {y^{\prime } c=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7329

ODE	\[ \boxed {y^{\prime } c=a} \]
program solution	\[ y = \frac {x a}{c}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {a x}{c}+c_{1} \]

Problem 7330

ODE	\[ \boxed {y^{\prime } c=a x} \]
program solution	\[ y = \frac {x^{2} a}{2 c}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {a \,x^{2}}{2 c}+c_{1} \]

Problem 7331

ODE	\[ \boxed {y^{\prime } c -y=a x} \]
program solution	\[ y = -\frac {\left ({\mathrm e}^{-\frac {x}{c}} a \,c^{2}+a x \,{\mathrm e}^{-\frac {x}{c}} c -c_{1} \right ) {\mathrm e}^{\frac {x}{c}}}{c} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{c}} c_{1} -a \left (c +x \right ) \]

Problem 7332

ODE	\[ \boxed {y^{\prime } c -b y=a x} \]
program solution	\[ y = -\frac {\left (a x \,{\mathrm e}^{-\frac {b x}{c}} b c +{\mathrm e}^{-\frac {b x}{c}} a \,c^{2}-c_{1} b^{2}\right ) {\mathrm e}^{\frac {b x}{c}}}{b^{2} c} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {b x}{c}} c_{1} b^{2}-a \left (b x +c \right )}{b^{2}} \]

Problem 7333

ODE	\[ \boxed {y^{\prime } c -y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {x}{c}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{c}} c_{1} \]

Problem 7334

ODE	\[ \boxed {y^{\prime } c -b y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{\frac {b x}{c}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{\frac {b x}{c}} c_{1} \]

Problem 7335

ODE	\[ \boxed {y^{\prime } c -b y^{2}=a x} \]
program solution	\[ y = \frac {\left (\operatorname {AiryAi}\left (1, -\left (\frac {a b}{c^{2}}\right )^{\frac {1}{3}} x \right ) c_{3} +\operatorname {AiryBi}\left (1, -\left (\frac {a b}{c^{2}}\right )^{\frac {1}{3}} x \right )\right ) \left (\frac {a b}{c^{2}}\right )^{\frac {1}{3}} c}{b \left (c_{3} \operatorname {AiryAi}\left (-\left (\frac {a b}{c^{2}}\right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (\frac {a b}{c^{2}}\right )^{\frac {1}{3}} x \right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\frac {b a}{c^{2}}\right )^{\frac {1}{3}} \left (\operatorname {AiryAi}\left (1, -\left (\frac {b a}{c^{2}}\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (1, -\left (\frac {b a}{c^{2}}\right )^{\frac {1}{3}} x \right )\right ) c}{b \left (c_{1} \operatorname {AiryAi}\left (-\left (\frac {b a}{c^{2}}\right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (\frac {b a}{c^{2}}\right )^{\frac {1}{3}} x \right )\right )} \]

Problem 7336

ODE	\[ \boxed {y^{\prime } c -\frac {a x +b y^{2}}{r}=0} \]
program solution	\[ y = \frac {\left (\operatorname {AiryAi}\left (1, -\left (\frac {a b}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right ) c_{3} +\operatorname {AiryBi}\left (1, -\left (\frac {a b}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )\right ) \left (\frac {a b}{r^{2} c^{2}}\right )^{\frac {1}{3}} c r}{b \left (c_{3} \operatorname {AiryAi}\left (-\left (\frac {a b}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (\frac {a b}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (\frac {b a}{r^{2} c^{2}}\right )^{\frac {1}{3}} \left (\operatorname {AiryAi}\left (1, -\left (\frac {b a}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right ) c_{1} +\operatorname {AiryBi}\left (1, -\left (\frac {b a}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )\right ) r c}{b \left (c_{1} \operatorname {AiryAi}\left (-\left (\frac {b a}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )+\operatorname {AiryBi}\left (-\left (\frac {b a}{r^{2} c^{2}}\right )^{\frac {1}{3}} x \right )\right )} \]

Problem 7337

ODE	\[ \boxed {y^{\prime } c -\frac {a x +b y^{2}}{x r}=0} \]
program solution	\[ y = \frac {\left (\operatorname {BesselJ}\left (1, \frac {2 \sqrt {a b}\, \sqrt {x}}{r c}\right ) c_{3} +\operatorname {BesselY}\left (1, \frac {2 \sqrt {a b}\, \sqrt {x}}{r c}\right )\right ) \sqrt {a b}\, \sqrt {x}}{b \left (c_{3} \operatorname {BesselJ}\left (0, \frac {2 \sqrt {a b}\, \sqrt {x}}{r c}\right )+\operatorname {BesselY}\left (0, \frac {2 \sqrt {a b}\, \sqrt {x}}{r c}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {\frac {x b a}{r^{2} c^{2}}}\, c r \left (\operatorname {BesselY}\left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right ) c_{1} +\operatorname {BesselJ}\left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )}{b \left (c_{1} \operatorname {BesselY}\left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )+\operatorname {BesselJ}\left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )} \]

Problem 7338

ODE	\[ \boxed {y^{\prime } c -\frac {a x +b y^{2}}{x^{2} r}=0} \]
program solution	\[ y = \frac {\left (\operatorname {BesselJ}\left (0, \frac {2 \sqrt {a b}}{r c \sqrt {x}}\right ) c_{3} +\operatorname {BesselY}\left (0, \frac {2 \sqrt {a b}}{r c \sqrt {x}}\right )\right ) \sqrt {x}\, \sqrt {a b}}{b \left (\operatorname {BesselY}\left (1, \frac {2 \sqrt {a b}}{r c \sqrt {x}}\right )+c_{3} \operatorname {BesselJ}\left (1, \frac {2 \sqrt {a b}}{r c \sqrt {x}}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {a \left (\operatorname {BesselY}\left (0, 2 \sqrt {\frac {b a}{c^{2} r^{2} x}}\right ) c_{1} +\operatorname {BesselJ}\left (0, 2 \sqrt {\frac {b a}{c^{2} r^{2} x}}\right )\right )}{c r \sqrt {\frac {b a}{c^{2} r^{2} x}}\, \left (c_{1} \operatorname {BesselY}\left (1, 2 \sqrt {\frac {b a}{c^{2} r^{2} x}}\right )+\operatorname {BesselJ}\left (1, 2 \sqrt {\frac {b a}{c^{2} r^{2} x}}\right )\right )} \]

Problem 7339

ODE	\[ \boxed {y^{\prime } c -\frac {a x +b y^{2}}{y}=0} \]
program solution	\[ \frac {c \left (2 b^{2} y^{2}+2 a b x +a c \right ) {\mathrm e}^{-\frac {2 b x}{c}}}{4 b^{2}} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 a x b -2 a c}}{2 b} \\ y \left (x \right ) &= \frac {\sqrt {4 \,{\mathrm e}^{\frac {2 b x}{c}} c_{1} b^{2}-4 a x b -2 a c}}{2 b} \\ \end{align*}

Problem 7340

ODE	\[ \boxed {a \sin \left (x \right ) y x y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7341

ODE	\[ \boxed {f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi =0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7342

ODE	\[ \boxed {y^{\prime }-y=\sin \left (x \right )} \]
program solution	\[ y = -\frac {{\mathrm e}^{x} \left ({\mathrm e}^{-x} \sin \left (x \right )+\cos \left (x \right ) {\mathrm e}^{-x}-2 c_{1} \right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\cos \left (x \right )}{2}-\frac {\sin \left (x \right )}{2}+c_{1} {\mathrm e}^{x} \]

Problem 7343

ODE	\[ \boxed {y^{\prime }-y^{2}=\sin \left (x \right )} \]
program solution	\[ y = \frac {-c_{3} \operatorname {MathieuCPrime}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )-\operatorname {MathieuSPrime}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )}{2 c_{3} \operatorname {MathieuC}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )+2 \operatorname {MathieuS}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-c_{1} \operatorname {MathieuSPrime}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )-\operatorname {MathieuCPrime}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )}{2 c_{1} \operatorname {MathieuS}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )+2 \operatorname {MathieuC}\left (0, -2, -\frac {\pi }{4}+\frac {x}{2}\right )} \]

Problem 7344

ODE	\[ \boxed {y^{\prime }-\frac {y}{x}=\cos \left (x \right )} \]
program solution	\[ y = x \left (\operatorname {Ci}\left (x \right )+c_{1} \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\operatorname {Ci}\left (x \right )+c_{1} \right ) x \]

Problem 7345

ODE	\[ \boxed {y^{\prime }-\frac {y^{2}}{x}=\cos \left (x \right )} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\textit {\_Y}^{\prime \prime }\left (x \right )+\frac {\textit {\_Y}^{\prime }\left (x \right )}{x}+\frac {\cos \left (x \right ) \textit {\_Y} \left (x \right )}{x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) x}{\operatorname {DESol}\left (\left \{\textit {\_Y}^{\prime \prime }\left (x \right )+\frac {\textit {\_Y}^{\prime }\left (x \right )}{x}+\frac {\cos \left (x \right ) \textit {\_Y} \left (x \right )}{x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 7346

ODE	\[ \boxed {y^{\prime }-y-b y^{2}=x} \]
program solution	\[ y = \frac {2 b^{\frac {1}{3}} \operatorname {AiryAi}\left (1, -\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{3} -\operatorname {AiryAi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{3} +2 b^{\frac {1}{3}} \operatorname {AiryBi}\left (1, -\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right )-\operatorname {AiryBi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right )}{2 b \left (\operatorname {AiryAi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{3} +\operatorname {AiryBi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 b^{\frac {1}{3}} \operatorname {AiryAi}\left (1, -\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1} +2 \operatorname {AiryBi}\left (1, -\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) b^{\frac {1}{3}}-\operatorname {AiryAi}\left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1} -\operatorname {AiryBi}\left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right )}{2 b \left (\operatorname {AiryAi}\left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right )\right )} \]

Problem 7347

ODE	\[ \boxed {x y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7348

ODE	\[ \boxed {5 y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7349

ODE	\[ \boxed {{\mathrm e} y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7350

ODE	\[ \boxed {\pi y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7351

ODE	\[ \boxed {y^{\prime } \sin \left (x \right )=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7352

ODE	\[ \boxed {f \left (x \right ) y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7353

ODE	\[ \boxed {x y^{\prime }=1} \]
program solution	\[ y = \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \ln \left (x \right )+c_{1} \]

Problem 7354

ODE	\[ \boxed {x y^{\prime }=\sin \left (x \right )} \]
program solution	\[ y = \operatorname {Si}\left (x \right )+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {Si}\left (x \right )+c_{1} \]

Problem 7355

ODE	\[ \boxed {\left (x -1\right ) y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7356

ODE	\[ \boxed {y^{\prime } y=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -c_{1} \\ \end{align*}

Problem 7357

ODE	\[ \boxed {x y^{\prime } y=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7358

ODE	\[ \boxed {x y \sin \left (x \right ) y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7359

ODE	\[ \boxed {\pi y \sin \left (x \right ) y^{\prime }=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7360

ODE	\[ \boxed {y^{\prime } \sin \left (x \right ) x=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7361

ODE	\[ \boxed {x \sin \left (x \right ) {y^{\prime }}^{2}=0} \]
program solution	\[ y = c_{1} \] Verified OK. \[ y = c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7362

ODE	\[ \boxed {y {y^{\prime }}^{2}=0} \]
program solution	\[ y = c_{1} \] Verified OK. \[ y = c_{2} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ \end{align*}

Problem 7363

ODE	\[ \boxed {{y^{\prime }}^{n}=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7364

ODE	\[ \boxed {x {y^{\prime }}^{n}=0} \]
program solution	\[ y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \]

Problem 7365

ODE	\[ \boxed {{y^{\prime }}^{2}=x} \]
program solution	\[ y = \frac {2 x^{\frac {3}{2}}}{3}+c_{1} \] Verified OK. \[ y = -\frac {2 x^{\frac {3}{2}}}{3}+c_{2} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {2 x^{\frac {3}{2}}}{3}+c_{1} \\ y \left (x \right ) &= -\frac {2 x^{\frac {3}{2}}}{3}+c_{1} \\ \end{align*}

Problem 7366

ODE	\[ \boxed {{y^{\prime }}^{2}-y=x} \]
program solution	\[ y = 1-x \] Verified OK. \[ y = {\left (-\operatorname {LambertW}\left (-{\mathrm e}^{-1} {\mathrm e}^{-\frac {x}{2}} c_{1} \right )-1\right )}^{2}-x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )^{2}+2 \operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-\frac {x}{2}-1}\right )-x +1 \]

Problem 7367

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {y}{x}=0} \]
program solution	\[ y = 0 \] Verified OK. \[ y = x \] Verified OK. \[ y = x \left (1+\frac {c_{1}}{\sqrt {x}}\right )^{2} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (x +\sqrt {c_{1} x}\right )^{2}}{x} \\ y \left (x \right ) &= \frac {\left (-x +\sqrt {c_{1} x}\right )^{2}}{x} \\ \end{align*}

Problem 7368

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {y^{2}}{x}=0} \]
program solution	\[ \frac {y \ln \left (y\right )}{\sqrt {y^{2}}} = 2 x \sqrt {\frac {1}{x}}+c_{1} \] Verified OK. {0 < 1/x, 0 < y^2} \[ -\frac {y \ln \left (y\right )}{\sqrt {y^{2}}} = 2 x \sqrt {\frac {1}{x}}+c_{1} \] Verified OK. {0 < 1/x, 0 < y^2}
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} {\mathrm e}^{-2 \sqrt {x}} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{2 \sqrt {x}} \\ \end{align*}

Problem 7369

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {y^{3}}{x}=0} \]
program solution	\[ y = \frac {8 x \sqrt {\frac {1}{x}}+4 c_{1}}{8 x^{3} \left (\frac {1}{x}\right )^{\frac {3}{2}}+6 x \sqrt {\frac {1}{x}}\, c_{1}^{2}+c_{1}^{3}+12 c_{1} x} \] Verified OK. \[ y = \frac {8 x \sqrt {\frac {1}{x}}+4 c_{1}}{8 x^{3} \left (\frac {1}{x}\right )^{\frac {3}{2}}+6 x \sqrt {\frac {1}{x}}\, c_{1}^{2}+c_{1}^{3}+12 c_{1} x} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\operatorname {WeierstrassP}\left (1, 0, 0\right ) 2^{\frac {2}{3}}}{\left (\sqrt {x}\, 2^{\frac {1}{3}}+c_{1} \right )^{2}} \\ \end{align*}

Problem 7370

ODE	\[ \boxed {{y^{\prime }}^{3}-\frac {y^{2}}{x}=0} \]
program solution	\[ y = \frac {x^{2}}{8}+\frac {x^{2} \left (\frac {1}{x}\right )^{\frac {2}{3}} c_{1}}{4}+\frac {x \left (\frac {1}{x}\right )^{\frac {1}{3}} c_{1}^{2}}{6}+\frac {c_{1}^{3}}{27} \] Verified OK. \[ y = \frac {x^{2}}{8}+\frac {x^{2} \left (\frac {1}{x}\right )^{\frac {2}{3}} c_{1}}{4}+\frac {x \left (\frac {1}{x}\right )^{\frac {1}{3}} c_{1}^{2}}{6}+\frac {c_{1}^{3}}{27} \] Verified OK. \[ y = \frac {x^{2}}{8}+\frac {x^{2} \left (\frac {1}{x}\right )^{\frac {2}{3}} c_{1}}{4}+\frac {x \left (\frac {1}{x}\right )^{\frac {1}{3}} c_{1}^{2}}{6}+\frac {c_{1}^{3}}{27} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {3 x^{\frac {4}{3}} c_{1}}{8}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{8}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{16}+\frac {3 c_{1} \left (1-i \sqrt {3}\right ) x^{\frac {4}{3}}}{16}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{16}+\frac {3 \left (1+i \sqrt {3}\right ) c_{1} x^{\frac {4}{3}}}{16}-\frac {c_{1}^{3}}{8}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 x^{\frac {4}{3}} c_{1}}{16}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 \left (i \sqrt {3}-1\right ) c_{1} x^{\frac {4}{3}}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 c_{1} \left (-i \sqrt {3}-1\right ) x^{\frac {4}{3}}}{32}+\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= -\frac {3 x^{\frac {4}{3}} c_{1}}{16}+\frac {3 x^{\frac {2}{3}} c_{1}^{2}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (-i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 c_{1} \left (1-i \sqrt {3}\right ) x^{\frac {4}{3}}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) c_{1}^{2} x^{\frac {2}{3}}}{64}+\frac {3 \left (1+i \sqrt {3}\right ) c_{1} x^{\frac {4}{3}}}{32}-\frac {c_{1}^{3}}{64}+\frac {x^{2}}{8} \\ \end{align*}

Problem 7371

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {1}{x y}=0} \]
program solution	\[ \frac {2 \ln \left (x^{\frac {3}{2}} y^{\frac {3}{2}}-3 x^{2}\right )}{3} = \ln \left (x \right )+c_{1} \] Verified OK. \[ \frac {2 \ln \left (x^{\frac {3}{2}} y^{\frac {3}{2}}+3 x^{2}\right )}{3} = \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\begin{align*} \frac {y \left (x \right ) \sqrt {x y \left (x \right )}-c_{1} \sqrt {x}-3 x}{\sqrt {x}} &= 0 \\ \frac {y \left (x \right ) \sqrt {x y \left (x \right )}-c_{1} \sqrt {x}+3 x}{\sqrt {x}} &= 0 \\ \end{align*}

Problem 7372

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {1}{x y^{3}}=0} \]
program solution	\[ \frac {2 \ln \left (x^{\frac {5}{2}} y^{\frac {5}{2}}-5 x^{3}\right )}{5} = \ln \left (x \right )+c_{1} \] Verified OK. \[ \frac {2 \ln \left (x^{\frac {5}{2}} y^{\frac {5}{2}}+5 x^{3}\right )}{5} = \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\begin{align*} \frac {\sqrt {x y \left (x \right )}\, y \left (x \right )^{2}-c_{1} \sqrt {x}-5 x}{\sqrt {x}} &= 0 \\ \frac {\sqrt {x y \left (x \right )}\, y \left (x \right )^{2}-c_{1} \sqrt {x}+5 x}{\sqrt {x}} &= 0 \\ \end{align*}

Problem 7373

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {1}{y^{3} x^{2}}=0} \]
program solution	\[ \frac {2 y^{\frac {5}{2}}}{5}-\ln \left (x \right )-c_{1} = 0 \] Verified OK. \[ \frac {2 y^{\frac {5}{2}}}{5}+\ln \left (x \right )-c_{2} = 0 \] Verified OK.
Maple solution	\begin{align*} \ln \left (x \right )-\frac {2 y \left (x \right )^{\frac {5}{2}}}{5}-c_{1} &= 0 \\ \ln \left (x \right )+\frac {2 y \left (x \right )^{\frac {5}{2}}}{5}-c_{1} &= 0 \\ \end{align*}

Problem 7374

ODE	\[ \boxed {{y^{\prime }}^{4}-\frac {1}{x y^{3}}=0} \]
program solution	\[ \frac {4 \ln \left (3 x^{\frac {21}{4}} y^{\frac {7}{4}}-7 x^{6}\right )}{7} = 3 \ln \left (x \right )+c_{1} \] Verified OK. \[ \frac {4 \ln \left (7 i x^{6}-3 x^{\frac {21}{4}} y^{\frac {7}{4}}\right )}{3} = 7 \ln \left (x \right )+c_{1} \] Verified OK. \[ \frac {4 \ln \left (3 x^{\frac {21}{4}} y^{\frac {7}{4}}+7 x^{6}\right )}{7} = 3 \ln \left (x \right )+c_{1} \] Verified OK. \[ \frac {4 \ln \left (7 i x^{6}+3 x^{\frac {21}{4}} y^{\frac {7}{4}}\right )}{3} = 7 \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\begin{align*} -\frac {7 x^{3}-3 y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}+c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {-7 x^{3}+3 i y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {7 x^{3}+3 i y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \frac {7 x^{3}+3 y \left (x \right ) \left (x^{3} y \left (x \right )\right )^{\frac {3}{4}}-c_{1} x^{\frac {9}{4}}}{x^{\frac {9}{4}}} &= 0 \\ \end{align*}

Problem 7375

ODE	\[ \boxed {{y^{\prime }}^{2}-\frac {1}{y^{4} x^{3}}=0} \]
program solution	\[ y = \left (\frac {3 c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \] Verified OK. \[ y = -\frac {\left (\frac {3 c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (\frac {3 c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \] Verified OK. \[ y = -\frac {\left (\frac {3 c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (\frac {3 c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \] Verified OK. \[ y = \left (\frac {3 \sqrt {x}\, c_{2} +6}{\sqrt {x}}\right )^{\frac {1}{3}} \] Verified OK. \[ y = -\frac {\left (\frac {3 \sqrt {x}\, c_{2} +6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (\frac {3 \sqrt {x}\, c_{2} +6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \] Verified OK. \[ y = -\frac {\left (\frac {3 \sqrt {x}\, c_{2} +6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (\frac {3 \sqrt {x}\, c_{2} +6}{\sqrt {x}}\right )^{\frac {1}{3}}}{2} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (\frac {c_{1} \sqrt {x}-6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ y \left (x \right ) &= \left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \\ y \left (x \right ) &= -\frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{2} \\ y \left (x \right ) &= \frac {\left (\frac {c_{1} \sqrt {x}+6}{\sqrt {x}}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{2} \\ \end{align*}

Problem 7376

ODE	\[ \boxed {y^{\prime }-\sqrt {1+6 x +y}=0} \]
program solution	\[ y = {\mathrm e}^{-2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_{1}}{12}-\frac {x}{12}-1}}{6}\right )+\frac {c_{1}}{6}-\frac {x}{6}-2}-12 \,{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_{1}}{12}-\frac {x}{12}-1}}{6}\right )+\frac {c_{1}}{12}-\frac {x}{12}-1}-6 x +35 \] Verified OK.
Maple solution	\[ x -2 \sqrt {1+6 x +y \left (x \right )}+6 \ln \left (6+\sqrt {1+6 x +y \left (x \right )}\right )-6 \ln \left (-6+\sqrt {1+6 x +y \left (x \right )}\right )+6 \ln \left (-35+y \left (x \right )+6 x \right )-c_{1} = 0 \]

Problem 7377

ODE	\[ \boxed {y^{\prime }-\left (1+6 x +y\right )^{\frac {1}{3}}=0} \]
program solution	\[ x = \frac {3 \left (1+6 x +y\right )^{\frac {2}{3}}}{2}-36 \ln \left (\left (1+6 x +y\right )^{\frac {2}{3}}-6 \left (1+6 x +y\right )^{\frac {1}{3}}+36\right )+72 \ln \left (\left (1+6 x +y\right )^{\frac {1}{3}}+6\right )+36 \ln \left (217+6 x +y\right )-18 \left (1+6 x +y\right )^{\frac {1}{3}}+c_{1} \] Verified OK.
Maple solution	\[ x -\frac {3 \left (1+6 x +y \left (x \right )\right )^{\frac {2}{3}}}{2}-72 \ln \left (6+\left (1+6 x +y \left (x \right )\right )^{\frac {1}{3}}\right )+36 \ln \left (\left (1+6 x +y \left (x \right )\right )^{\frac {2}{3}}-6 \left (1+6 x +y \left (x \right )\right )^{\frac {1}{3}}+36\right )-36 \ln \left (217+y \left (x \right )+6 x \right )+18 \left (1+6 x +y \left (x \right )\right )^{\frac {1}{3}}-c_{1} = 0 \]

Problem 7378

ODE	\[ \boxed {y^{\prime }-\left (1+6 x +y\right )^{\frac {1}{4}}=0} \]
program solution	\[ x = -216 \ln \left (1295-6 x -y\right )-12 \sqrt {1+6 x +y}-216 \ln \left (-36+\sqrt {1+6 x +y}\right )+216 \ln \left (\sqrt {1+6 x +y}+36\right )+144 \left (1+6 x +y\right )^{\frac {1}{4}}+432 \ln \left (-6+\left (1+6 x +y\right )^{\frac {1}{4}}\right )-432 \ln \left (\left (1+6 x +y\right )^{\frac {1}{4}}+6\right )+\frac {4 \left (1+6 x +y\right )^{\frac {3}{4}}}{3}+c_{1} \] Verified OK.
Maple solution	\[ x +216 \ln \left (-y \left (x \right )-6 x +1295\right )+12 \sqrt {1+6 x +y \left (x \right )}+216 \ln \left (\sqrt {1+6 x +y \left (x \right )}-36\right )-216 \ln \left (\sqrt {1+6 x +y \left (x \right )}+36\right )-144 \left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}+432 \ln \left (6+\left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}\right )-432 \ln \left (\left (1+6 x +y \left (x \right )\right )^{\frac {1}{4}}-6\right )-\frac {4 \left (1+6 x +y \left (x \right )\right )^{\frac {3}{4}}}{3}-c_{1} = 0 \]

Problem 7379

ODE	\[ \boxed {y^{\prime }-\left (a +x b +y\right )^{4}=0} \]
program solution	\[ x = \int _{}^{y}\frac {1}{\left (x b +\textit {\_a} \right )^{4}+4 \left (x b +\textit {\_a} \right )^{3} a +6 \left (x b +\textit {\_a} \right )^{2} a^{2}+4 \left (x b +\textit {\_a} \right ) a^{3}+a^{4}+b}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -b x +\operatorname {RootOf}\left (-x +\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{4}+4 \textit {\_a}^{3} a +6 \textit {\_a}^{2} a^{2}+4 \textit {\_a} \,a^{3}+a^{4}+b}d \textit {\_a} +c_{1} \right ) \]

Problem 7380

ODE	\[ \boxed {y^{\prime }-\left (\pi +x +7 y\right )^{\frac {7}{2}}=0} \]
program solution	\[ x -7 \left (\int _{}^{y}\frac {1}{7 \left (\pi +x +7 \textit {\_a} \right )^{\frac {7}{2}}+1}d \textit {\_a} \right )-c_{1} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x}{7}+\operatorname {RootOf}\left (-x +7 \left (\int _{}^{\textit {\_Z}}\frac {1}{1+7 \left (\pi +7 \textit {\_a} \right )^{\frac {7}{2}}}d \textit {\_a} \right )+c_{1} \right ) \]

Problem 7381

ODE	\[ \boxed {y^{\prime }-\left (a +x b +y c \right )^{6}=0} \]
program solution	\[ x = \int _{}^{\frac {y c +x b}{c}}\frac {c}{\textit {\_a}^{6} c^{7}+6 \textit {\_a}^{5} a \,c^{6}+15 \textit {\_a}^{4} a^{2} c^{5}+20 \textit {\_a}^{3} a^{3} c^{4}+15 \textit {\_a}^{2} a^{4} c^{3}+6 \textit {\_a} \,a^{5} c^{2}+a^{6} c +b}d \textit {\_a} +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{c^{7} \textit {\_a}^{6}+6 \textit {\_a}^{5} a \,c^{6}+15 \textit {\_a}^{4} a^{2} c^{5}+20 \textit {\_a}^{3} a^{3} c^{4}+15 \textit {\_a}^{2} a^{4} c^{3}+6 \textit {\_a} \,a^{5} c^{2}+a^{6} c +b}d \textit {\_a} \right ) c -x +c_{1} \right ) c -b x}{c} \]

Problem 7382

ODE	\[ \boxed {y^{\prime }-{\mathrm e}^{x +y}=0} \]
program solution	\[ y = -\ln \left (-{\mathrm e}^{x}-c_{1} \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \ln \left (-\frac {1}{{\mathrm e}^{x}+c_{1}}\right ) \]

Problem 7383

ODE	\[ \boxed {y^{\prime }-{\mathrm e}^{x +y}=10} \]
program solution	\[ y = 10 x +\ln \left (-\frac {11}{-11+{\mathrm e}^{11 x +\frac {11 c_{1}}{2}}}\right )+\frac {11 c_{1}}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x +\ln \left (11\right )+\ln \left (\frac {{\mathrm e}^{11 x}}{-{\mathrm e}^{11 x}+c_{1}}\right ) \]

Problem 7384

ODE	\[ \boxed {y^{\prime }-10 \,{\mathrm e}^{x +y}=x^{2}} \]
program solution	\[ y = -\ln \left ({\mathrm e}^{-\frac {x^{3}}{3}} \left (-10 \left (\int {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}d x \right )+c_{1} \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{3}}{3}-\ln \left (-c_{1} -10 \left (\int {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}d x \right )\right ) \]

Problem 7385

ODE	\[ \boxed {y^{\prime }-{\mathrm e}^{x +y} x=\sin \left (x \right )} \]
program solution	\[ y = -\ln \left ({\mathrm e}^{\cos \left (x \right )} \left (-\left (\int x \,{\mathrm e}^{x -\cos \left (x \right )}d x \right )+c_{1} \right )\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\cos \left (x \right )-\ln \left (-c_{1} -\left (\int x \,{\mathrm e}^{x -\cos \left (x \right )}d x \right )\right ) \]

Problem 7386

ODE	\[ \boxed {y^{\prime }-5 \,{\mathrm e}^{x^{2}+20 y}=\sin \left (x \right )} \]
program solution	\[ y = -\frac {\ln \left ({\mathrm e}^{20 \cos \left (x \right )} \left (-100 \left (\int {\mathrm e}^{x^{2}-20 \cos \left (x \right )}d x \right )+c_{1} \right )\right )}{20} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\cos \left (x \right )-\frac {\ln \left (20\right )}{20}-\frac {\ln \left (-c_{1} -5 \left (\int {\mathrm e}^{x^{2}-20 \cos \left (x \right )}d x \right )\right )}{20} \]

Problem 7387

ODE	\begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+t\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= -3 t -2+c_{1} {\mathrm e}^{t} \\ y \left (t \right ) &= 2 t +1-\frac {c_{1} {\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{t}}{2} \\ \end{align*}

Problem 7388

ODE	\begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+t -{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+5 y \left (t \right )-t +2 \,{\mathrm e}^{t} \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2} +{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1} -3 t -11 \\ y \left (t \right ) &= -\frac {{\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2} \sqrt {3}}{2}+\frac {{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1} \sqrt {3}}{2}-\frac {3 \,{\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2}}{2}-\frac {3 \,{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1}}{2}-\frac {{\mathrm e}^{t}}{2}+2 t +7 \\ \end{align*}

Problem 7389

ODE	\begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+t +\sin \left (t \right )+\cos \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= -\sin \left (t \right )-3 \cos \left (t \right )+c_{1} {\mathrm e}^{t}-3 t -2 \\ y \left (t \right ) &= \sin \left (t \right )+2 \cos \left (t \right )-\frac {c_{1} {\mathrm e}^{t}}{2}+2 t +1-\frac {{\mathrm e}^{t}}{2} \\ \end{align*}

Problem 7390

ODE	\[ \boxed {y^{\prime \prime }=0} \]
program solution	\[ y = c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7391

ODE	\[ \boxed {{y^{\prime \prime }}^{2}=0} \]
program solution	\[ y = c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7392

ODE	\[ \boxed {{y^{\prime \prime }}^{n}=0} \]
program solution	\[ y = c_{1} x +c_{3} \] Verified OK. \[ y = x c_{2} +c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7393

ODE	\[ \boxed {a y^{\prime \prime }=0} \]
program solution	\[ y = c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7394

ODE	\[ \boxed {a {y^{\prime \prime }}^{2}=0} \]
program solution	\[ y = c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7395

ODE	\[ \boxed {a {y^{\prime \prime }}^{n}=0} \]
program solution	\[ y = c_{1} x +c_{3} \] Verified OK. \[ y = x c_{2} +c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]

Problem 7396

ODE	\[ \boxed {y^{\prime \prime }=1} \]
program solution	\[ y = \frac {x \left (x +2 c_{1} \right )}{2}+c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{2} x^{2}+c_{1} x +c_{2} \]

Problem 7397

ODE	\[ \boxed {{y^{\prime \prime }}^{2}=1} \]
program solution	\[ y = -\frac {1}{2} x^{2}+c_{1} x +c_{2} \] Verified OK. \[ y = \frac {1}{2} x^{2}+c_{3} x +c_{4} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {1}{2} x^{2}+c_{1} x +c_{2} \\ y \left (x \right ) &= -\frac {1}{2} x^{2}+c_{1} x +c_{2} \\ \end{align*}

Problem 7398

ODE	\[ \boxed {y^{\prime \prime }=x} \]
program solution	\[ y = \frac {1}{6} x^{3}+c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{6} x^{3}+c_{1} x +c_{2} \]

Problem 7399

ODE	\[ \boxed {{y^{\prime \prime }}^{2}=x} \]
program solution	\[ y = \frac {4 x^{\frac {5}{2}}}{15}+c_{1} x +c_{2} \] Verified OK. \[ y = -\frac {4 x^{\frac {5}{2}}}{15}+c_{3} x +c_{4} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {4 x^{\frac {5}{2}}}{15}+c_{1} x +c_{2} \\ y \left (x \right ) &= -\frac {4 x^{\frac {5}{2}}}{15}+c_{1} x +c_{2} \\ \end{align*}

Problem 7400

ODE	\[ \boxed {{y^{\prime \prime }}^{3}=0} \]
program solution	\[ y = c_{1} x +c_{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} x +c_{2} \]