2.17.107 Problems 10601 to 10700

Problem 10601

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

Problem 10602

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}-g \left (x \right ) y=a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y}^{\prime \prime }\left (x \right )-\frac {\left (f^{\prime }\left (x \right )+g \left (x \right ) f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right ) \left (a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right )\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} x^{1+2 n} \textit {\_Y} \left (x \right ) a^{2}+\textit {\_Y}^{\prime \prime }\left (x \right ) x f \left (x \right )-f \left (x \right )^{2} g \left (x \right ) x^{n +1} \textit {\_Y} \left (x \right ) a -\left (f^{\prime }\left (x \right )+g \left (x \right ) f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right ) x +f \left (x \right )^{2} x^{n} \textit {\_Y} \left (x \right ) a n}{x f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10603

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+a \,x^{n} g \left (x \right ) y=a n \,x^{n -1}+a^{2} x^{2 n} \left (g \left (x \right )-f \left (x \right )\right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y}^{\prime \prime }\left (x \right )-\frac {\left (-f \left (x \right ) g \left (x \right ) x^{n} a +f^{\prime }\left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right ) \left (-a^{2} x^{2 n} f \left (x \right )+a^{2} x^{2 n} g \left (x \right )+a n \,x^{n -1}\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{2} \textit {\_Y} \left (x \right ) a^{2} \left (f \left (x \right )-g \left (x \right )\right ) x^{1+2 n}+f \left (x \right )^{2} x^{n} \textit {\_Y} \left (x \right ) a n +a \,x^{n +1} f \left (x \right ) g \left (x \right ) \textit {\_Y}^{\prime }\left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right ) x +\textit {\_Y}^{\prime \prime }\left (x \right ) x f \left (x \right )}{f \left (x \right ) x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10604

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

Problem 10605

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y=a \lambda \,{\mathrm e}^{\lambda x}} \]
program solution	\[ y = \frac {\left (a \left (c_{3} +\int f \left (x \right ) {\mathrm e}^{a \left (\int f \left (x \right ) {\mathrm e}^{\lambda x}d x \right )}d x \right ) {\mathrm e}^{\lambda x -a \left (\int f \left (x \right ) {\mathrm e}^{\lambda x}d x \right )}-1\right ) {\mathrm e}^{a \left (\int f \left (x \right ) {\mathrm e}^{\lambda x}d x \right )}}{c_{3} +\int f \left (x \right ) {\mathrm e}^{a \left (\int f \left (x \right ) {\mathrm e}^{\lambda x}d x \right )}d x} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10606

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda x} \textit {\_Y} \left (x \right ) a^{2}+f \left (x \right )^{2} {\mathrm e}^{\lambda x} \textit {\_Y} \left (x \right ) a \lambda +\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda x} \textit {\_Y} \left (x \right ) a^{2}+f \left (x \right )^{2} {\mathrm e}^{\lambda x} \textit {\_Y} \left (x \right ) a \lambda +\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10607

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

Problem 10608

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right ) y=a \lambda \,{\mathrm e}^{\lambda x}} \]
program solution	\[ y = \frac {\left (a \,{\mathrm e}^{\lambda x}+b \right ) \left (\int f \left (x \right ) {\mathrm e}^{\int f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right )d x}d x \right )+a c_{3} {\mathrm e}^{\lambda x}+c_{3} b -{\mathrm e}^{\int f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right )d x}}{c_{3} +\int f \left (x \right ) {\mathrm e}^{\int f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right )d x}d x} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10609

ODE	\[ \boxed {y^{\prime }-{\mathrm e}^{\lambda x} f \left (x \right ) y^{2}-\left (a f \left (x \right )-\lambda \right ) y=b \,{\mathrm e}^{-\lambda x} f \left (x \right )} \]
program solution	\[ y = -\frac {\left (a^{2}+\tanh \left (\frac {\sqrt {a^{2} \left (a^{2}-4 b \right )}\, \left (a \left (\int f \left (x \right )d x \right )+c_{3} \right )}{2 a^{2}}\right ) \sqrt {a^{2} \left (a^{2}-4 b \right )}\right ) {\mathrm e}^{-\lambda x}}{2 a} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (a^{2}+\tanh \left (\frac {\sqrt {a^{2} \left (a^{2}-4 b \right )}\, \left (a \left (\int f \left (x \right )d x \right )+c_{1} \right )}{2 a^{2}}\right ) \sqrt {a^{2} \left (a^{2}-4 b \right )}\right ) {\mathrm e}^{-x \lambda }}{2 a} \]

Problem 10610

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}-g \left (x \right ) y=a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda x} \textit {\_Y} \left (x \right ) a^{2}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+a f \left (x \right )^{2} \textit {\_Y} \left (x \right ) \left (\lambda -g \left (x \right )\right ) {\mathrm e}^{\lambda x}-\left (f^{\prime }\left (x \right )+g \left (x \right ) f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda x} \textit {\_Y} \left (x \right ) a^{2}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+a f \left (x \right )^{2} \textit {\_Y} \left (x \right ) \left (\lambda -g \left (x \right )\right ) {\mathrm e}^{\lambda x}-\left (f^{\prime }\left (x \right )+g \left (x \right ) f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10611

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+a \,{\mathrm e}^{\lambda x} g \left (x \right ) y=a \lambda \,{\mathrm e}^{\lambda x}+a^{2} {\mathrm e}^{2 \lambda x} \left (g \left (x \right )-f \left (x \right )\right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-a^{2} f \left (x \right )^{2} \textit {\_Y} \left (x \right ) \left (f \left (x \right )-g \left (x \right )\right ) {\mathrm e}^{2 \lambda x}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+f \left (x \right ) a \left (\lambda f \left (x \right ) \textit {\_Y} \left (x \right )+g \left (x \right ) \textit {\_Y}^{\prime }\left (x \right )\right ) {\mathrm e}^{\lambda x}-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-a^{2} f \left (x \right )^{2} \textit {\_Y} \left (x \right ) \left (f \left (x \right )-g \left (x \right )\right ) {\mathrm e}^{2 \lambda x}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+f \left (x \right ) a \left (\lambda f \left (x \right ) \textit {\_Y} \left (x \right )+g \left (x \right ) \textit {\_Y}^{\prime }\left (x \right )\right ) {\mathrm e}^{\lambda x}-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10612

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda \,x^{2}} \textit {\_Y} \left (x \right ) a^{2}+2 f \left (x \right )^{2} {\mathrm e}^{\lambda \,x^{2}} \textit {\_Y} \left (x \right ) a \lambda x +\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} {\mathrm e}^{2 \lambda \,x^{2}} \textit {\_Y} \left (x \right ) a^{2}+2 f \left (x \right )^{2} {\mathrm e}^{\lambda \,x^{2}} \textit {\_Y} \left (x \right ) a \lambda x +\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10613

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}-\lambda x y=a \,{\mathrm e}^{\lambda x} f \left (x \right )} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+f \left (x \right )^{3} {\mathrm e}^{\lambda x} a \textit {\_Y} \left (x \right )-\left (f \left (x \right ) \lambda x +f^{\prime }\left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+f \left (x \right )^{3} {\mathrm e}^{\lambda x} a \textit {\_Y} \left (x \right )-\left (f \left (x \right ) \lambda x +f^{\prime }\left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10614

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-a \tanh \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda } \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10615

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-a \coth \left (\lambda x \right )^{2} \left (a f \left (x \right )+\lambda \right )+a \lambda } \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10616

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-f \left (x \right ) a^{2}+\sinh \left (\lambda x \right ) a \lambda -f \left (x \right ) \sinh \left (\lambda x \right )^{2} a^{2}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} \cosh \left (\lambda x \right )^{2} \textit {\_Y} \left (x \right ) a^{2}+f \left (x \right )^{2} \sinh \left (\lambda x \right ) \textit {\_Y} \left (x \right ) a \lambda -f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} \cosh \left (\lambda x \right )^{2} \textit {\_Y} \left (x \right ) a^{2}+f \left (x \right )^{2} \sinh \left (\lambda x \right ) \textit {\_Y} \left (x \right ) a \lambda -f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right ) f \left (x \right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10617

ODE	\[ \boxed {x y^{\prime }-f \left (x \right ) y^{2}=a -a^{2} f \left (x \right ) \ln \left (x \right )^{2}} \]
program solution	\[ y = -\frac {\left (\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{-\frac {f \left (x \right )^{3} \ln \left (x \right )^{2} \textit {\_Y} \left (x \right ) a^{2}-f \left (x \right )^{2} a \textit {\_Y} \left (x \right )-\textit {\_Y}^{\prime \prime }\left (x \right ) x^{2} f \left (x \right )+f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right ) x^{2}-f \left (x \right ) \textit {\_Y}^{\prime }\left (x \right ) x}{x^{2} f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) x}{f \left (x \right ) \operatorname {DESol}\left (\left \{-\frac {f \left (x \right )^{3} \ln \left (x \right )^{2} \textit {\_Y} \left (x \right ) a^{2}-f \left (x \right )^{2} a \textit {\_Y} \left (x \right )-\textit {\_Y}^{\prime \prime }\left (x \right ) x^{2} f \left (x \right )+f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right ) x^{2}-f \left (x \right ) \textit {\_Y}^{\prime }\left (x \right ) x}{x^{2} f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10618

ODE	\[ \boxed {x y^{\prime }-f \left (x \right ) \left (y+a \ln \left (x \right )\right )^{2}=-a} \]
program solution	\[ y = -\frac {\left (\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x^{2} f \left (x \right )-2 x \left (f \left (x \right )^{2} \ln \left (x \right ) a +\frac {x f^{\prime }\left (x \right )}{2}-\frac {f \left (x \right )}{2}\right ) \textit {\_Y}^{\prime }\left (x \right )+f \left (x \right )^{2} a \left (f \left (x \right ) \ln \left (x \right )^{2} a -1\right ) \textit {\_Y} \left (x \right )}{x^{2} f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) x}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x^{2} f \left (x \right )-2 x \left (f \left (x \right )^{2} \ln \left (x \right ) a +\frac {x f^{\prime }\left (x \right )}{2}-\frac {f \left (x \right )}{2}\right ) \textit {\_Y}^{\prime }\left (x \right )+f \left (x \right )^{2} a \left (f \left (x \right ) \ln \left (x \right )^{2} a -1\right ) \textit {\_Y} \left (x \right )}{x^{2} f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -a \ln \left (x \right )+\frac {1}{c_{1} -\left (\int \frac {f \left (x \right )}{x}d x \right )} \]

Problem 10619

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+a x \ln \left (x \right ) f \left (x \right ) y=a \ln \left (x \right )+a} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+\left (x f \left (x \right )^{2} \ln \left (x \right ) a -f^{\prime }\left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )+a \left (\ln \left (x \right )+1\right ) f \left (x \right )^{2} \textit {\_Y} \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )+\left (x f \left (x \right )^{2} \ln \left (x \right ) a -f^{\prime }\left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )+a \left (\ln \left (x \right )+1\right ) f \left (x \right )^{2} \textit {\_Y} \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10620

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

Problem 10621

ODE	\[ \boxed {y^{\prime }-\lambda \sin \left (\lambda x \right ) y^{2}-f \left (x \right ) \cos \left (\lambda x \right ) y=-f \left (x \right )} \]
program solution	\[ y = \frac {\sec \left (\lambda x \right ) \lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (\lambda x \right )+2 \lambda \tan \left (\lambda x \right )\right )d x} \sin \left (\lambda x \right )d x \right )-\sec \left (\lambda x \right ) c_{3} -{\mathrm e}^{\int \left (f \left (x \right ) \cos \left (\lambda x \right )+2 \lambda \tan \left (\lambda x \right )\right )d x}}{\lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (\lambda x \right )+2 \lambda \tan \left (\lambda x \right )\right )d x} \sin \left (\lambda x \right )d x \right )-c_{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sec \left (x \lambda \right ) \lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x} \sin \left (x \lambda \right )d x \right ) c_{1} -c_{1} {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x}-\sec \left (x \lambda \right )}{\lambda \left (\int {\mathrm e}^{\int \left (f \left (x \right ) \cos \left (x \lambda \right )+2 \tan \left (x \lambda \right ) \lambda \right )d x} \sin \left (x \lambda \right )d x \right ) c_{1} -1} \]

Problem 10622

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-f \left (x \right ) a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {f \left (x \right )^{2} \sin \left (\lambda x \right ) \textit {\_Y} \left (x \right ) a \lambda -f \left (x \right )^{3} \textit {\_Y} \left (x \right ) a^{2} \cos \left (\lambda x \right )^{2}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {f \left (x \right )^{2} \sin \left (\lambda x \right ) \textit {\_Y} \left (x \right ) a \lambda -f \left (x \right )^{3} \textit {\_Y} \left (x \right ) a^{2} \cos \left (\lambda x \right )^{2}+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )-f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right ) f \left (x \right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10623

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-f \left (x \right ) a^{2}+a \cos \left (\lambda x \right ) \lambda +f \left (x \right ) a^{2} \cos \left (\lambda x \right )^{2}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} \textit {\_Y} \left (x \right ) \sin \left (\lambda x \right )^{2} a^{2}+\textit {\_Y} \left (x \right ) f \left (x \right )^{2} \cos \left (\lambda x \right ) a \lambda -f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {-f \left (x \right )^{3} \textit {\_Y} \left (x \right ) \sin \left (\lambda x \right )^{2} a^{2}+\textit {\_Y} \left (x \right ) f \left (x \right )^{2} \cos \left (\lambda x \right ) a \lambda -f^{\prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )}{f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right ) f \left (x \right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10624

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda } \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10625

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}=-a \cot \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda } \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10626

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

Problem 10627

ODE	\[ \boxed {y^{\prime }-f \left (x \right ) y^{2}+f \left (x \right ) g \left (x \right ) y=g^{\prime }\left (x \right )} \]
program solution	\[ y = \frac {\left (\int f \left (x \right ) {\mathrm e}^{\int g \left (x \right ) f \left (x \right )d x}d x \right ) g \left (x \right )+c_{3} g \left (x \right )-{\mathrm e}^{\int g \left (x \right ) f \left (x \right )d x}}{c_{3} +\int f \left (x \right ) {\mathrm e}^{\int g \left (x \right ) f \left (x \right )d x}d x} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10628

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

Problem 10629

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

Problem 10630

ODE	\[ \boxed {y^{\prime }-\frac {f^{\prime }\left (x \right ) y^{2}}{g \left (x \right )}=-\frac {g^{\prime }\left (x \right )}{f \left (x \right )}} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) g \left (x \right ) f \left (x \right ) f^{\prime }\left (x \right )-f \left (x \right ) g \left (x \right ) f^{\prime \prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+f^{\prime }\left (x \right ) g^{\prime }\left (x \right ) \left (\textit {\_Y}^{\prime }\left (x \right ) f \left (x \right )-\textit {\_Y} \left (x \right ) f^{\prime }\left (x \right )\right )}{g \left (x \right ) f^{\prime }\left (x \right ) f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) g \left (x \right )}{f^{\prime }\left (x \right ) \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) g \left (x \right ) f \left (x \right ) f^{\prime }\left (x \right )-f \left (x \right ) g \left (x \right ) f^{\prime \prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+f^{\prime }\left (x \right ) g^{\prime }\left (x \right ) \left (\textit {\_Y}^{\prime }\left (x \right ) f \left (x \right )-\textit {\_Y} \left (x \right ) f^{\prime }\left (x \right )\right )}{g \left (x \right ) f^{\prime }\left (x \right ) f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\left (\int \frac {\frac {d}{d x}f \left (x \right )}{g \left (x \right ) f \left (x \right )^{2}}d x \right ) g \left (x \right ) f \left (x \right )-c_{1} f \left (x \right ) g \left (x \right )-1}{f \left (x \right )^{2} \left (\int \frac {\frac {d}{d x}f \left (x \right )}{g \left (x \right ) f \left (x \right )^{2}}d x +c_{1} \right )} \]

Problem 10631

ODE	\[ \boxed {f \left (x \right )^{2} y^{\prime }-f^{\prime }\left (x \right ) y^{2}+g \left (x \right ) \left (-f \left (x \right )+y\right )=0} \]
program solution	\[ y = -\frac {\left (\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {2 {f^{\prime }\left (x \right )}^{2} f \left (x \right )^{2} \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )^{3} f^{\prime }\left (x \right )-f \left (x \right )^{3} f^{\prime \prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+{f^{\prime }\left (x \right )}^{2} g \left (x \right ) \textit {\_Y} \left (x \right )+f^{\prime }\left (x \right ) g \left (x \right ) f \left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )^{3} f^{\prime }\left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\right ) f \left (x \right )^{2}}{f^{\prime }\left (x \right ) \operatorname {DESol}\left (\left \{\frac {2 {f^{\prime }\left (x \right )}^{2} f \left (x \right )^{2} \textit {\_Y}^{\prime }\left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) f \left (x \right )^{3} f^{\prime }\left (x \right )-f \left (x \right )^{3} f^{\prime \prime }\left (x \right ) \textit {\_Y}^{\prime }\left (x \right )+{f^{\prime }\left (x \right )}^{2} g \left (x \right ) \textit {\_Y} \left (x \right )+f^{\prime }\left (x \right ) g \left (x \right ) f \left (x \right ) \textit {\_Y}^{\prime }\left (x \right )}{f \left (x \right )^{3} f^{\prime }\left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10632

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

Problem 10633

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

Problem 10634

ODE	\[ \boxed {y^{\prime }-y^{2}=-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {-\left (\int \frac {1}{f \left (x \right )^{2}}d x \right ) \left (\frac {d}{d x}f \left (x \right )\right ) f \left (x \right )-\left (\frac {d}{d x}f \left (x \right )\right ) c_{1} f \left (x \right )-1}{\left (\int \frac {1}{f \left (x \right )^{2}}d x +c_{1} \right ) f \left (x \right )^{2}} \]

Problem 10635

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

Problem 10636

ODE	\[ \boxed {y^{\prime }-y^{2}=\frac {f \left (\frac {1}{x}\right )}{x^{4}}} \]
program solution	\[ y = -\frac {\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x^{4}+f \left (\frac {1}{x}\right ) \textit {\_Y} \left (x \right )}{x^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x^{4}+f \left (\frac {1}{x}\right ) \textit {\_Y} \left (x \right )}{x^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10637

ODE	\[ \boxed {y^{\prime }-y^{2}=\frac {f \left (\frac {a x +b}{c x +d}\right )}{\left (c x +d \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {f \left (\frac {a x +b}{c x +d}\right ) \textit {\_Y} \left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) \left (c x +d \right )^{4}}{\left (c x +d \right )^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {f \left (\frac {a x +b}{c x +d}\right ) \textit {\_Y} \left (x \right )+\textit {\_Y}^{\prime \prime }\left (x \right ) \left (c x +d \right )^{4}}{\left (c x +d \right )^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10638

ODE	\[ \boxed {x^{2} y^{\prime }-x^{4} f \left (x \right ) y^{2}=1} \]
program solution	\[ y = -\frac {\frac {d}{d x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x f \left (x \right )+\left (-x f^{\prime }\left (x \right )-2 f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )+f \left (x \right )^{2} \textit {\_Y} \left (x \right ) x}{x f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{f \left (x \right ) x^{2} \operatorname {DESol}\left (\left \{\frac {\textit {\_Y}^{\prime \prime }\left (x \right ) x f \left (x \right )+\left (-x f^{\prime }\left (x \right )-2 f \left (x \right )\right ) \textit {\_Y}^{\prime }\left (x \right )+f \left (x \right )^{2} \textit {\_Y} \left (x \right ) x}{x f \left (x \right )}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10639

ODE	\[ \boxed {x^{2} y^{\prime }-y^{2} x^{4}=x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\left (x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4}\right ) \textit {\_Y} \left (x \right )-\frac {2 \textit {\_Y}^{\prime }\left (x \right )}{x}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{x^{2} \operatorname {DESol}\left (\left \{\frac {4 x^{1+2 n} \textit {\_Y} \left (x \right ) f \left (a \,x^{n}+b \right )+4 \textit {\_Y}^{\prime \prime }\left (x \right ) x -8 \textit {\_Y}^{\prime }\left (x \right )+x \left (-n^{2}+1\right ) \textit {\_Y} \left (x \right )}{4 x}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10640

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

Problem 10641

ODE	\[ \boxed {y^{\prime }-y^{2}={\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\lambda ^{2}}{4}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) {\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\textit {\_Y} \left (x \right ) \lambda ^{2}}{4}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) {\mathrm e}^{2 \lambda x} f \left ({\mathrm e}^{\lambda x}\right )-\frac {\textit {\_Y} \left (x \right ) \lambda ^{2}}{4}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10642

ODE	\[ \boxed {y^{\prime }-y^{2}=-\frac {\lambda ^{2}}{4}+\frac {{\mathrm e}^{2 \lambda x} f \left (\frac {a \,{\mathrm e}^{\lambda x}+b}{c \,{\mathrm e}^{\lambda x}+d}\right )}{\left (c \,{\mathrm e}^{\lambda x}+d \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {\textit {\_Y} \left (x \right ) {\mathrm e}^{2 \lambda x} f \left (\frac {a \,{\mathrm e}^{\lambda x}+b}{c \,{\mathrm e}^{\lambda x}+d}\right )+6 \left (-\frac {\textit {\_Y} \left (x \right ) \lambda ^{2}}{4}+\textit {\_Y}^{\prime \prime }\left (x \right )\right ) \left (c^{2} d^{2} {\mathrm e}^{2 \lambda x}+\frac {2 \,{\mathrm e}^{3 \lambda x} c^{3} d}{3}+\frac {{\mathrm e}^{4 \lambda x} c^{4}}{6}+\frac {2 d^{3} \left (c \,{\mathrm e}^{\lambda x}+\frac {d}{4}\right )}{3}\right )}{{\mathrm e}^{4 \lambda x} c^{4}+4 \,{\mathrm e}^{3 \lambda x} c^{3} d +6 c^{2} d^{2} {\mathrm e}^{2 \lambda x}+4 c \,{\mathrm e}^{\lambda x} d^{3}+d^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {\textit {\_Y} \left (x \right ) {\mathrm e}^{2 \lambda x} f \left (\frac {a \,{\mathrm e}^{\lambda x}+b}{c \,{\mathrm e}^{\lambda x}+d}\right )+6 \left (-\frac {\textit {\_Y} \left (x \right ) \lambda ^{2}}{4}+\textit {\_Y}^{\prime \prime }\left (x \right )\right ) \left (c^{2} d^{2} {\mathrm e}^{2 \lambda x}+\frac {2 \,{\mathrm e}^{3 \lambda x} c^{3} d}{3}+\frac {{\mathrm e}^{4 \lambda x} c^{4}}{6}+\frac {2 d^{3} \left (c \,{\mathrm e}^{\lambda x}+\frac {d}{4}\right )}{3}\right )}{{\mathrm e}^{4 \lambda x} c^{4}+4 \,{\mathrm e}^{3 \lambda x} c^{3} d +6 c^{2} d^{2} {\mathrm e}^{2 \lambda x}+4 c \,{\mathrm e}^{\lambda x} d^{3}+d^{4}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10643

ODE	\[ \boxed {y^{\prime }-y^{2}=-\lambda ^{2}+\frac {f \left (\coth \left (\lambda x \right )\right )}{\sinh \left (\lambda x \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \operatorname {csch}\left (\lambda x \right )^{4} f \left (\coth \left (\lambda x \right )\right )-\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \operatorname {csch}\left (\lambda x \right )^{4} f \left (\coth \left (\lambda x \right )\right )-\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10644

ODE	\[ \boxed {y^{\prime }-y^{2}=-\lambda ^{2}+\frac {f \left (\tanh \left (\lambda x \right )\right )}{\cosh \left (\lambda x \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) f \left (\tanh \left (\lambda x \right )\right ) \operatorname {sech}\left (\lambda x \right )^{4}-\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) f \left (\tanh \left (\lambda x \right )\right ) \operatorname {sech}\left (\lambda x \right )^{4}-\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10645

ODE	\[ \boxed {x^{2} y^{\prime }-x^{2} y^{2}=f \left (a \ln \left (x \right )+b \right )+\frac {1}{4}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\frac {4 \textit {\_Y}^{\prime \prime }\left (x \right ) x^{2}+4 \textit {\_Y} \left (x \right ) f \left (a \ln \left (x \right )+b \right )+\textit {\_Y} \left (x \right )}{4 x^{2}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\frac {4 \textit {\_Y}^{\prime \prime }\left (x \right ) x^{2}+4 \textit {\_Y} \left (x \right ) f \left (a \ln \left (x \right )+b \right )+\textit {\_Y} \left (x \right )}{4 x^{2}}\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10646

ODE	\[ \boxed {y^{\prime }-y^{2}=\lambda ^{2}+\frac {f \left (\cot \left (\lambda x \right )\right )}{\sin \left (\lambda x \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )+\csc \left (\lambda x \right )^{4} \textit {\_Y} \left (x \right ) f \left (\cot \left (\lambda x \right )\right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )+\csc \left (\lambda x \right )^{4} \textit {\_Y} \left (x \right ) f \left (\cot \left (\lambda x \right )\right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10647

ODE	\[ \boxed {y^{\prime }-y^{2}=\lambda ^{2}+\frac {f \left (\tan \left (\lambda x \right )\right )}{\cos \left (\lambda x \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \sec \left (\lambda x \right )^{4} f \left (\tan \left (\lambda x \right )\right )+\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \sec \left (\lambda x \right )^{4} f \left (\tan \left (\lambda x \right )\right )+\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10648

ODE	\[ \boxed {y^{\prime }-y^{2}=\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}}} \]
program solution	\[ y = -\frac {\frac {\partial }{\partial x}\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )+\csc \left (\lambda x +b \right )^{4} f \left (\csc \left (\lambda x +b \right ) \sin \left (\lambda x +a \right )\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )}{\operatorname {DESol}\left (\left \{\textit {\_Y} \left (x \right ) \lambda ^{2}+\textit {\_Y}^{\prime \prime }\left (x \right )+\csc \left (\lambda x +b \right )^{4} f \left (\csc \left (\lambda x +b \right ) \sin \left (\lambda x +a \right )\right ) \textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )} \] Verified OK.
Maple solution	\[ \text {No solution found} \]

Problem 10649

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

Problem 10650

ODE	\[ \boxed {y y^{\prime }-y=A x +B} \]
program solution	\[ \frac {B \left (\ln \left (A^{2} x^{2}+\left (2 B x +y \left (x -y\right )\right ) A +B \left (B +y\right )\right ) \sqrt {4 A +1}+2 \,\operatorname {arctanh}\left (\frac {\left (x -2 y\right ) A +B}{\sqrt {4 A +1}\, \left (A x +B \right )}\right )\right )}{2 \sqrt {4 A +1}\, A} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (x A +B \right ) \operatorname {RootOf}\left (\textit {\_Z}^{2}-A +\textit {\_Z} +{\mathrm e}^{\operatorname {RootOf}\left (\left (x A +B \right )^{2} \left (-2 \,{\mathrm e}^{\textit {\_Z}} \cosh \left (\left (\textit {\_Z} +2 \ln \left (x A +B \right )+2 c_{1} \right ) \sqrt {4 A +1}\right )+4 A -2 \,{\mathrm e}^{\textit {\_Z}}+1\right )\right )}\right )}{A} \]

Problem 10651

ODE	\[ \boxed {y y^{\prime }-y=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}}} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {9 \left (A \sqrt {x}+B -\frac {2 x^{\frac {3}{2}}}{9}\right ) A}{3 A \sqrt {x}+3 \operatorname {RootOf}\left (18 A^{3} \left (\int _{}^{\textit {\_Z}}\frac {1}{-2 \textit {\_a}^{3} B^{2}+9 \textit {\_a} \,A^{3}-9 A^{3}}d \textit {\_a} \right )-9 A \left (\int \frac {1}{9 x A -2 x^{2}+9 B \sqrt {x}}d x \right )+2 c_{1} \right ) B} \]

Problem 10652

ODE	\[ \boxed {y y^{\prime }-y=2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ \frac {-\sqrt {\frac {-6 A^{2}-8 A \sqrt {x}-2 x +2 y \left (x \right )}{y \left (x \right )}}\, \sqrt {2}+4 \sqrt {-\frac {A^{2}}{y \left (x \right )}}\, \operatorname {arctanh}\left (\frac {\sqrt {-\frac {A^{2}}{y \left (x \right )}}\, \left (3 A +\sqrt {x}\right )}{\sqrt {\frac {-3 A^{2}-4 A \sqrt {x}-x +y \left (x \right )}{y \left (x \right )}}\, A}\right )+c_{1} \sqrt {-\frac {A^{2}}{y \left (x \right )}}}{\sqrt {-\frac {A^{2}}{y \left (x \right )}}} = 0 \]

Problem 10653

ODE	\[ \boxed {y y^{\prime }-y=A x +\frac {B}{x}-\frac {B^{2}}{x^{3}}} \]
program solution
Maple solution	\[ \frac {\left (-y \left (x \right ) x^{2} B -B^{2} x \right ) \left (\int _{}^{-\frac {x^{2}}{2 y \left (x \right ) x +2 B}}\frac {{\mathrm e}^{\frac {2 \,\operatorname {arctanh}\left (\frac {4 A \textit {\_a} -1}{\sqrt {4 A +1}}\right )}{\sqrt {4 A +1}}} \left (4 A \,\textit {\_a}^{2}-2 \textit {\_a} -1\right )}{\textit {\_a}^{2}}d \textit {\_a} \right )+2 y \left (x \right ) \left (-y \left (x \right )^{2} x^{2}+\left (x^{3}-2 B x \right ) y \left (x \right )+A \,x^{4}+B \,x^{2}-B^{2}\right ) {\mathrm e}^{-\frac {2 \,\operatorname {arctanh}\left (\frac {2 A \,x^{2}+y \left (x \right ) x +B}{\sqrt {4 A +1}\, \left (y \left (x \right ) x +B \right )}\right )}{\sqrt {4 A +1}}}+x c_{1} \left (y \left (x \right ) x +B \right )}{x \left (y \left (x \right ) x +B \right )} = 0 \]

Problem 10654

ODE	\[ \boxed {y y^{\prime }-y=A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{-1+2 k}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10655

ODE	\[ \boxed {y y^{\prime }-y=\frac {A}{x}-\frac {A^{2}}{x^{3}}} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {\left (-c_{1} x^{2}+A \,{\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} A \,{\mathrm e}^{2 \textit {\_Z}}-x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x^{2} {\mathrm e}^{\textit {\_Z}}-c_{1}^{2} x^{2}-2 A \,{\mathrm e}^{2 \textit {\_Z}}+2 A c_{1} {\mathrm e}^{\textit {\_Z}}\right )}\right ) {\mathrm e}^{-\operatorname {RootOf}\left (2 \textit {\_Z} A \,{\mathrm e}^{2 \textit {\_Z}}-x^{2} {\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x^{2} {\mathrm e}^{\textit {\_Z}}-c_{1}^{2} x^{2}-2 A \,{\mathrm e}^{2 \textit {\_Z}}+2 A c_{1} {\mathrm e}^{\textit {\_Z}}\right )}}{x} \]

Problem 10656

ODE	\[ \boxed {y y^{\prime }-y=A +B \,{\mathrm e}^{-\frac {2 x}{A}}} \]
program solution
Maple solution	\[ c_{1} -2 \arctan \left (\frac {y \left (x \right )+A}{y \left (x \right ) \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \left (x \right )+A \right )^{2}}{y \left (x \right )^{2}}}}\right ) A -2 \sqrt {\frac {-A B \,{\mathrm e}^{-\frac {2 x}{A}}-\left (y \left (x \right )+A \right )^{2}}{y \left (x \right )^{2}}}\, y \left (x \right ) = 0 \]

Problem 10657

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

Problem 10658

ODE	\[ \boxed {y y^{\prime }-y=-\frac {2 \left (1+m \right )}{\left (m +3\right )^{2}}+A \,x^{m}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10659

ODE	\[ \boxed {y y^{\prime }-y=-\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {-108 A^{3}-54 A^{2} \sqrt {x}+2 x^{\frac {3}{2}}}{3 \,{\mathrm e}^{\operatorname {RootOf}\left (36 A^{2} {\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+18 A^{2} {\mathrm e}^{\textit {\_Z}} \ln \left (\frac {\left (3 A -\sqrt {x}\right ) \left (6 A -\sqrt {x}\right ) \left (36 A^{2}-x \right )}{\left (9 A^{2}-x \right ) \left (6 A +\sqrt {x}\right ) \left (3 A +\sqrt {x}\right ) \left ({\mathrm e}^{\textit {\_Z}}+9\right )^{2}}\right )+108 A^{2} c_{1} {\mathrm e}^{\textit {\_Z}}+36 A^{2} {\mathrm e}^{\textit {\_Z}} \textit {\_Z} +6 A \sqrt {x}\, {\mathrm e}^{\textit {\_Z}} \ln \left (2\right )+3 A \sqrt {x}\, {\mathrm e}^{\textit {\_Z}} \ln \left (\frac {\left (3 A -\sqrt {x}\right ) \left (6 A -\sqrt {x}\right ) \left (36 A^{2}-x \right )}{\left (9 A^{2}-x \right ) \left (6 A +\sqrt {x}\right ) \left (3 A +\sqrt {x}\right ) \left ({\mathrm e}^{\textit {\_Z}}+9\right )^{2}}\right )+18 A \sqrt {x}\, c_{1} {\mathrm e}^{\textit {\_Z}}+6 A \sqrt {x}\, {\mathrm e}^{\textit {\_Z}} \textit {\_Z} +108 A^{2} {\mathrm e}^{\textit {\_Z}}-18 A \sqrt {x}\, {\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} x \ln \left (\frac {\left (3 A -\sqrt {x}\right ) \left (6 A -\sqrt {x}\right ) \left (36 A^{2}-x \right )}{\left (9 A^{2}-x \right ) \left (6 A +\sqrt {x}\right ) \left (3 A +\sqrt {x}\right ) \left ({\mathrm e}^{\textit {\_Z}}+9\right )^{2}}\right )-6 c_{1} x \,{\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z} x +324 A^{2}+54 A \sqrt {x}-18 x \right )} A +9 A +3 \sqrt {x}} \]

Problem 10660

ODE	\[ \boxed {y y^{\prime }-y=\frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (m +3\right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (m +3\right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10661

ODE	\[ \boxed {y y^{\prime }-y=\frac {\left (1+2 m \right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}}} \]
program solution
Maple solution	\[ \frac {2^{-\frac {m}{1+m}} y \left (x \right ) \left (\frac {-2 y \left (x \right ) m x -2 A m -x^{2}}{2 y \left (x \right ) x +2 A}\right )^{\frac {1}{1+m}} \left (y \left (x \right ) x +A \right ) \left (\frac {\left (-1-2 m \right ) x^{2}+2 y \left (x \right ) m x +2 A m}{y \left (x \right ) x +A}\right )^{\frac {1+2 m}{1+m}}-x \left (A \left (\int _{}^{-\frac {x^{2}}{2 y \left (x \right ) x +2 A}}\frac {\left (-m +\textit {\_a} \right )^{\frac {1}{1+m}} \left (\left (2 \textit {\_a} +1\right ) m +\textit {\_a} \right )^{\frac {1+2 m}{1+m}}}{\textit {\_a}^{2}}d \textit {\_a} \right )-c_{1} \right )}{x} = 0 \]

Problem 10662

ODE	\[ \boxed {y y^{\prime }-y=\frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3}} \]
program solution
Maple solution	\[ -\frac {27 \left (A y \left (x \right ) 3^{\frac {1}{4}} \left (x A +\frac {1}{3}\right ) {\left (\frac {A \left (9 A^{2} x^{2}-9 y \left (x \right ) A +9 x A +2\right ) \left (3 A \,x^{2}+3 y \left (x \right )+x \right )}{\left (-9 y \left (x \right ) A +3 x A +1\right )^{2}}\right )}^{\frac {1}{4}}-\frac {\left (\int _{}^{\frac {\left (3 x A +1\right )^{2}}{-9 y \left (x \right ) A +3 x A +1}}\frac {\left (\textit {\_a}^{2}-1\right )^{\frac {1}{4}}}{\sqrt {\textit {\_a}}}d \textit {\_a} +c_{1} \right ) \left (\frac {1}{3}-3 y \left (x \right ) A +x A \right ) \sqrt {\frac {\left (3 x A +1\right )^{2}}{-9 y \left (x \right ) A +3 x A +1}}}{9}\right )}{\sqrt {\frac {\left (3 x A +1\right )^{2}}{-9 y \left (x \right ) A +3 x A +1}}\, \left (-9 y \left (x \right ) A +3 x A +1\right )} = 0 \]

Problem 10663

ODE	\[ \boxed {y y^{\prime }-y=-\frac {3 x}{16}+\frac {5 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10664

ODE	\[ \boxed {y y^{\prime }-y=\frac {A}{x}} \]
program solution
Maple solution	\[ \frac {\operatorname {erf}\left (\frac {\left (y \left (x \right )-x \right ) \sqrt {2}}{2 \sqrt {-A}}\right ) \sqrt {2}\, \sqrt {\pi }\, x -2 \,{\mathrm e}^{\frac {\left (y \left (x \right )-x \right )^{2}}{2 A}} \sqrt {-A}+c_{1} x}{x} = 0 \]

Problem 10665

ODE	\[ \boxed {y y^{\prime }-y=-\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4}} \]
program solution
Maple solution	\[ -\frac {3 \left (-4 \left (\left (\int _{}^{\frac {6 A \sqrt {x}-2 x +3 y \left (x \right )}{12 A^{2}-4 A \sqrt {x}+2 y \left (x \right )}}\frac {{\mathrm e}^{-\frac {2}{2 \textit {\_a} +1}} \sqrt {2 \textit {\_a} +1}}{\sqrt {2 \textit {\_a} -3}}d \textit {\_a} \right ) A +\frac {c_{1}}{2}\right ) \left (A^{2}-\frac {A \sqrt {x}}{3}+\frac {y \left (x \right )}{6}\right ) \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}+\frac {\sqrt {\frac {3 A^{2}+2 A \sqrt {x}-x +2 y \left (x \right )}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}\, y \left (x \right ) {\mathrm e}^{\frac {-6 A^{2}+2 A \sqrt {x}-y \left (x \right )}{3 A^{2}+2 A \sqrt {x}-x +2 y \left (x \right )}} \left (3 A -\sqrt {x}\right )}{3}\right )}{\sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}\, \left (6 A^{2}-2 A \sqrt {x}+y \left (x \right )\right )} = 0 \]

Problem 10666

ODE	\[ \boxed {y y^{\prime }-y=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}}} \]
program solution
Maple solution	\[ \frac {512 \left (-\frac {33 \left (a^{4}+\frac {23}{66} a^{2} x^{2}+\frac {1}{66} x^{4}\right ) x \sqrt {8 a^{2}+x^{2}}}{64}+a^{6}+\frac {75 a^{4} x^{2}}{64}+\frac {27 a^{2} x^{4}}{128}+\frac {x^{6}}{128}\right ) {\mathrm e}^{-\frac {\left (-y \left (x \right )+x \right )^{2} \left (-64 \sqrt {8 a^{2}+x^{2}}\, a^{6}-108 \sqrt {8 a^{2}+x^{2}}\, a^{4} x^{2}-25 \sqrt {8 a^{2}+x^{2}}\, a^{2} x^{4}-\sqrt {8 a^{2}+x^{2}}\, x^{6}+328 a^{6} x +200 a^{4} x^{3}+29 a^{2} x^{5}+x^{7}\right )^{2}}{2 \left (128 a^{6}+150 a^{4} x^{2}-66 \sqrt {8 a^{2}+x^{2}}\, a^{4} x +27 a^{2} x^{4}-23 \sqrt {8 a^{2}+x^{2}}\, a^{2} x^{3}+x^{6}-\sqrt {8 a^{2}+x^{2}}\, x^{5}\right )^{2} a^{2} \left (-\sqrt {8 a^{2}+x^{2}}\, x +4 a^{2}+x^{2}\right )}} a -128 \left (\sqrt {2}\, \sqrt {\pi }\, \operatorname {erf}\left (\frac {\left (-y \left (x \right )+x \right ) \sqrt {2}\, \left (-\left (-64 a^{6}-108 a^{4} x^{2}-25 a^{2} x^{4}-x^{6}\right ) \sqrt {8 a^{2}+x^{2}}-328 a^{6} x -200 a^{4} x^{3}-29 a^{2} x^{5}-x^{7}\right )}{2 \sqrt {-\sqrt {8 a^{2}+x^{2}}\, x +4 a^{2}+x^{2}}\, \left (\left (-66 x \,a^{5}-23 a^{3} x^{3}-a \,x^{5}\right ) \sqrt {8 a^{2}+x^{2}}+128 a^{7}+150 a^{5} x^{2}+27 a^{3} x^{4}+a \,x^{6}\right )}\right )-c_{1} \right ) \left (\frac {\left (\left (a^{4}+\frac {21}{32} a^{2} x^{2}+\frac {1}{32} x^{4}\right ) y \left (x \right )-\frac {33 \left (a^{4}+\frac {23}{66} a^{2} x^{2}+\frac {1}{66} x^{4}\right ) x}{16}\right ) \sqrt {8 a^{2}+x^{2}}}{4}+\frac {\left (-25 a^{4} x -\frac {25}{4} a^{2} x^{3}-\frac {1}{4} x^{5}\right ) y \left (x \right )}{32}+a^{6}+\frac {75 a^{4} x^{2}}{64}+\frac {27 a^{2} x^{4}}{128}+\frac {x^{6}}{128}\right ) \sqrt {-\sqrt {8 a^{2}+x^{2}}\, x +4 a^{2}+x^{2}}}{\sqrt {-\sqrt {8 a^{2}+x^{2}}\, x +4 a^{2}+x^{2}}\, \left (\left (\left (32 a^{4}+21 a^{2} x^{2}+x^{4}\right ) y \left (x \right )-66 a^{4} x -23 a^{2} x^{3}-x^{5}\right ) \sqrt {8 a^{2}+x^{2}}+\left (-100 a^{4} x -25 a^{2} x^{3}-x^{5}\right ) y \left (x \right )+128 a^{6}+150 a^{4} x^{2}+27 a^{2} x^{4}+x^{6}\right )} = 0 \]

Problem 10667

ODE	\[ \boxed {y y^{\prime }-y=2 x +\frac {A}{x^{2}}} \]
program solution
Maple solution	\[ \frac {6 \left (\sqrt {3}\, \operatorname {arctanh}\left (\frac {\sqrt {\frac {x \left (A^{2}\right )^{\frac {1}{3}}}{A}}\, \left (-2 x +y \left (x \right )\right )}{\sqrt {\frac {\left (4 x^{3}-4 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) \left (A^{2}\right )^{\frac {1}{3}}}{y \left (x \right )^{2} A}}\, y \left (x \right )}\right ) A +\frac {c_{1}}{6}\right ) x \sqrt {\frac {x \left (A^{2}\right )^{\frac {1}{3}}}{A}}+2 \sqrt {3}\, y \left (x \right ) \left (-x^{3}-\frac {y \left (x \right ) x^{2}}{2}+\frac {y \left (x \right )^{2} x}{2}+A \right ) \sqrt {\frac {\left (4 x^{3}-4 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) \left (A^{2}\right )^{\frac {1}{3}}}{y \left (x \right )^{2} A}}}{\sqrt {\frac {x \left (A^{2}\right )^{\frac {1}{3}}}{A}}\, x} = 0 \]

Problem 10668

ODE	\[ \boxed {y y^{\prime }-y=-\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10669

ODE	\[ \boxed {y y^{\prime }-y=\frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10670

ODE	\[ \boxed {y y^{\prime }-y=-\frac {4 x}{25}+\frac {A}{\sqrt {x}}} \]
program solution
Maple solution	\[ \frac {625 \sqrt {A \,x^{\frac {3}{2}}}\, c_{1} \left (-\frac {A y \left (x \right )^{2} \sqrt {x}}{2}+\frac {16 x^{4}}{625}-\frac {16 x^{3} y \left (x \right )}{125}+\frac {6 y \left (x \right )^{2} x^{2}}{25}-\frac {x y \left (x \right )^{3}}{5}+\frac {y \left (x \right )^{4}}{16}+A^{2} x +\frac {4 A y \left (x \right ) x^{\frac {3}{2}}}{5}-\frac {8 A \,x^{\frac {5}{2}}}{25}\right ) \sqrt {\frac {A \sqrt {x}-\frac {4 \left (x -\frac {5 y \left (x \right )}{4}\right )^{2}}{25}}{\sqrt {x}\, A}}+\frac {625 \left (y \left (x \right )^{4}-10 A^{2} y \left (x \right )\right ) x^{\frac {3}{2}}}{2}+500 \left (-y \left (x \right )^{3}+4 A^{2}\right ) x^{\frac {5}{2}}+\frac {128 x^{\frac {11}{2}}}{5}+400 y \left (x \right )^{2} x^{\frac {7}{2}}-160 y \left (x \right ) x^{\frac {9}{2}}+\frac {625 \left (-\frac {y \left (x \right )^{5}}{2}+5 A^{2} y \left (x \right )^{2}\right ) \sqrt {x}}{4}-400 A \,x^{4}+1500 A y \left (x \right ) x^{3}-1875 A y \left (x \right )^{2} x^{2}+\frac {3125 A y \left (x \right )^{3} x}{4}-3125 A^{3} x}{\sqrt {A \,x^{\frac {3}{2}}}\, \sqrt {\frac {A \sqrt {x}-\frac {4 \left (x -\frac {5 y \left (x \right )}{4}\right )^{2}}{25}}{\sqrt {x}\, A}}\, \left (25 A \sqrt {x}-4 \left (x -\frac {5 y \left (x \right )}{4}\right )^{2}\right )^{2}} = 0 \]

Problem 10671

ODE	\[ \boxed {y y^{\prime }-y=-\frac {9 x}{100}+\frac {A}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10672

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ \frac {\left (3 A -\sqrt {x}\right ) \left (36 A^{4}+120 A^{3} \sqrt {x}-80 A \,x^{\frac {3}{2}}+52 A^{2} x +84 A^{2} y \left (x \right )+140 A \sqrt {x}\, y \left (x \right )+16 x^{2}-56 y \left (x \right ) x +49 y \left (x \right )^{2}\right ) y \left (x \right )}{8 \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}\, \left (\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y \left (x \right )}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}\right )^{\frac {3}{2}} \left (6 A^{2}-2 A \sqrt {x}+y \left (x \right )\right )^{3} A}+\frac {\left (-54 A^{2}-6 A \sqrt {x}+8 x -21 y \left (x \right )\right ) \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}}{\sqrt {\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y \left (x \right )}{6 A^{2}-2 A \sqrt {x}+y \left (x \right )}}\, \left (36 A^{2}-12 A \sqrt {x}+6 y \left (x \right )\right )}+c_{1} = 0 \]

Problem 10673

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10674

ODE	\[ \boxed {y y^{\prime }-y=-\frac {2 x}{9}+\frac {A}{\sqrt {x}}} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {2 \,3^{\frac {5}{6}} 2^{\frac {1}{3}} \left (-2 x^{\frac {3}{2}}+9 A \right )}{\sqrt {x}\, \left (\left (27 \tan \left (\operatorname {RootOf}\left (18 \,3^{\frac {5}{6}} 2^{\frac {1}{3}} \left (\int \frac {\left (\frac {A}{x^{\frac {3}{2}}}\right )^{\frac {2}{3}} \sqrt {x}}{-2 x^{\frac {3}{2}}+9 A}d x \right )+\ln \left (-8 \sqrt {3}\, \sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )^{3}-8 \cos \left (\textit {\_Z} \right )^{4}-4 \sqrt {3}\, \sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )+16 \cos \left (\textit {\_Z} \right )^{2}+1\right ) \sqrt {3}-12 \sqrt {3}\, c_{1} -12 \textit {\_Z} \right )\right )-9 \sqrt {3}\right ) \left (\frac {A}{x^{\frac {3}{2}}}\right )^{\frac {1}{3}}-6 \,2^{\frac {1}{3}} 3^{\frac {5}{6}}\right )} \]

Problem 10675

ODE	\[ \boxed {y y^{\prime }-y=-\frac {5 x}{36}+\frac {A}{x^{\frac {7}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10676

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10677

ODE	\[ \boxed {y y^{\prime }-y=-\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10678

ODE	\[ \boxed {y y^{\prime }-y=-\frac {3 x}{16}+\frac {A}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10679

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10680

ODE	\[ \boxed {y y^{\prime }-y=\frac {A}{\sqrt {x}}} \]
program solution
Maple solution	\[ \frac {\left (\operatorname {AiryBi}\left (-\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right ) c_{1} -\operatorname {AiryAi}\left (-\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right )\right ) 2^{\frac {2}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {1}{3}}-2 A \left (-\operatorname {AiryBi}\left (1, -\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right ) c_{1} +\operatorname {AiryAi}\left (1, -\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right )\right )}{2^{\frac {2}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {1}{3}} \operatorname {AiryBi}\left (-\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right )+2 \operatorname {AiryBi}\left (1, -\frac {2^{\frac {1}{3}} \left (-A^{2} x^{\frac {3}{2}}\right )^{\frac {2}{3}} \left (y \left (x \right )-x \right )}{2 A^{2} x}\right ) A} = 0 \]

Problem 10681

ODE	\[ \boxed {y y^{\prime }-y=\frac {A}{x^{2}}} \]
program solution
Maple solution	\[ \frac {-\left (\operatorname {AiryBi}\left (-\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right ) c_{1} -\operatorname {AiryAi}\left (-\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right )\right ) A \left (-y \left (x \right )+x \right ) 2^{\frac {1}{3}}+2 \left (-A^{2}\right )^{\frac {2}{3}} \left (\operatorname {AiryBi}\left (1, -\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right ) c_{1} -\operatorname {AiryAi}\left (1, -\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right )\right )}{-A 2^{\frac {1}{3}} \left (-y \left (x \right )+x \right ) \operatorname {AiryBi}\left (-\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right )+2 \operatorname {AiryBi}\left (1, -\frac {\left (x^{3}-2 y \left (x \right ) x^{2}+y \left (x \right )^{2} x +2 A \right ) 2^{\frac {2}{3}}}{4 \left (-A^{2}\right )^{\frac {1}{3}} x}\right ) \left (-A^{2}\right )^{\frac {2}{3}}} = 0 \]

Problem 10682

ODE	\[ \boxed {y y^{\prime }-y=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (n +3\right ) A^{2}}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ \frac {\left (n +2\right ) \left (\operatorname {BesselI}\left (\frac {3+n}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right ) c_{1} +\operatorname {BesselK}\left (\frac {3+n}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )\right ) A \sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}+\left (c_{1} \operatorname {BesselI}\left (\frac {1}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )-\operatorname {BesselK}\left (\frac {1}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )\right ) \left (\sqrt {x}+\left (n +1\right ) A \right )}{A \sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\, \left (n +2\right ) \operatorname {BesselI}\left (\frac {3+n}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )+\left (\sqrt {x}+\left (n +1\right ) A \right ) \operatorname {BesselI}\left (\frac {1}{n +2}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+A^{2} \left (n^{2}+4 n +3\right )+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )} = 0 \]

Problem 10683

ODE	\[ \boxed {y y^{\prime }-y=A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ \frac {-\left (n +2\right ) \left (\operatorname {BesselI}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}+1, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right ) c_{1} +\operatorname {BesselK}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}+1, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )\right ) A \sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}+\left (c_{1} \operatorname {BesselI}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )-\operatorname {BesselK}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )\right ) \left (A \sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}\, \left (n +2\right )-\sqrt {x}+\left (-n -2\right ) A \right )}{-A \sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\, \left (n +2\right ) \operatorname {BesselI}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}+1, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right )+\operatorname {BesselI}\left (\sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}, -\sqrt {\frac {2 \left (n +2\right ) A \sqrt {x}+\left (2 n +3\right ) A^{2}+x -y \left (x \right )}{\left (n +2\right )^{2} A^{2}}}\right ) \left (A \sqrt {\frac {\left (n +1\right )^{2}}{\left (n +2\right )^{2}}}\, \left (n +2\right )-\sqrt {x}+\left (-n -2\right ) A \right )} = 0 \]

Problem 10684

ODE	\[ \boxed {y y^{\prime }-y=A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}}} \]
program solution
Maple solution	\[ \frac {-c_{1} \left (\sqrt {\frac {A^{3}-B}{A^{3}}}\, A -A -\sqrt {x}\right ) \operatorname {BesselI}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right )+A \sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\, \operatorname {BesselI}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}+1, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right ) c_{1} +A \sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\, \operatorname {BesselK}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}+1, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right )+\operatorname {BesselK}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right ) \left (\sqrt {\frac {A^{3}-B}{A^{3}}}\, A -A -\sqrt {x}\right )}{A \sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\, \operatorname {BesselI}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}+1, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right )+\left (-\sqrt {\frac {A^{3}-B}{A^{3}}}\, A +A +\sqrt {x}\right ) \operatorname {BesselI}\left (\sqrt {\frac {A^{3}-B}{A^{3}}}, -\sqrt {\frac {2 A^{2} \sqrt {x}-y \left (x \right ) A +x A +B}{A^{3}}}\right )} = 0 \]

Problem 10685

ODE	\[ \boxed {y y^{\prime }-y=2 A^{2}-A \sqrt {x}} \]
program solution
Maple solution	\[ \frac {\left (-2 A +\sqrt {x}\right ) \operatorname {BesselK}\left (1, -\sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right )+\operatorname {BesselK}\left (0, -\sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\, A +c_{1} \left (A \operatorname {BesselI}\left (0, \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}+\left (-2 A +\sqrt {x}\right ) \operatorname {BesselI}\left (1, \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right )\right )}{A \operatorname {BesselI}\left (0, \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right ) \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}+\left (-2 A +\sqrt {x}\right ) \operatorname {BesselI}\left (1, \sqrt {-\frac {2 A \sqrt {x}-x +y \left (x \right )}{A^{2}}}\right )} = 0 \]

Problem 10686

ODE	\[ \boxed {y y^{\prime }-y=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10687

ODE	\[ \boxed {y y^{\prime }-y=-\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10688

ODE	\[ \boxed {y y^{\prime }-y=-\frac {3 x}{16}+\frac {3 A}{x^{\frac {1}{3}}}-\frac {12 A^{2}}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10689

ODE	\[ \boxed {y y^{\prime }-y=\frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10690

ODE	\[ \boxed {y y^{\prime }-y=\frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10691

ODE	\[ \boxed {y y^{\prime }-y=-\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10692

ODE	\[ \boxed {y y^{\prime }-y=A \,x^{2}-\frac {9}{625 A}} \]
program solution
Maple solution	\[ \frac {-\frac {125 \,2^{\frac {5}{6}} \left (\frac {-46875 A^{2} y \left (x \right )^{2}+\left (37500 A^{2} x +4500 A \right ) y \left (x \right )+31250 \left (x A -\frac {3}{25}\right ) \left (x A +\frac {3}{25}\right )^{2}}{\left (50 x A -125 y \left (x \right ) A +6\right )^{2}}\right )^{\frac {1}{6}} A y \left (x \right ) \sqrt {25 x A +3}}{2}+50 \left (x A -\frac {5 y \left (x \right ) A}{2}+\frac {3}{25}\right ) \left (\frac {\left (25 x A +3\right )^{\frac {3}{2}}}{50 x A -125 y \left (x \right ) A +6}\right )^{\frac {1}{3}} \left (\int _{}^{-\frac {2 \left (25 x A +3\right )^{\frac {3}{2}}}{125 y \left (x \right ) A -50 x A -6}}\frac {\left (\textit {\_a}^{2}-6\right )^{\frac {1}{6}}}{\textit {\_a}^{\frac {1}{3}}}d \textit {\_a} +c_{1} \right )}{\left (\frac {\left (25 x A +3\right )^{\frac {3}{2}}}{50 x A -125 y \left (x \right ) A +6}\right )^{\frac {1}{3}} \left (50 x A -125 y \left (x \right ) A +6\right )} = 0 \]

Problem 10693

ODE	\[ \boxed {y y^{\prime }-y=-\frac {6}{25} x -A \,x^{2}} \]
program solution
Maple solution	\[ c_{1} +\frac {\left (2 x -5 y \left (x \right )\right ) \left (\int _{}^{-\frac {10 \sqrt {-x A}\, x}{-2 x +5 y \left (x \right )}}\frac {\left (\textit {\_a}^{2}-6\right )^{\frac {1}{6}}}{\textit {\_a}^{\frac {1}{3}}}d \textit {\_a} \right )-\frac {5 \,2^{\frac {5}{6}} \left (\frac {-50 A \,x^{3}-12 x^{2}+60 y \left (x \right ) x -75 y \left (x \right )^{2}}{\left (-2 x +5 y \left (x \right )\right )^{2}}\right )^{\frac {1}{6}} 5^{\frac {2}{3}} \sqrt {-x A}\, y \left (x \right )}{2 \left (-\frac {\sqrt {-x A}\, x}{-2 x +5 y \left (x \right )}\right )^{\frac {1}{3}}}}{2 x -5 y \left (x \right )} = 0 \]

Problem 10694

ODE	\[ \boxed {y y^{\prime }-y=\frac {6}{25} x -A \,x^{2}} \]
program solution
Maple solution	\[ -\frac {125 \left (5^{\frac {1}{3}} 2^{\frac {5}{6}} {\left (-\frac {1250 \left (\frac {3 y \left (x \right )^{2} A}{2}+\left (-\frac {6 x A}{5}+\frac {36}{125}\right ) y \left (x \right )+\left (x A -\frac {6}{25}\right )^{2} x \right ) A}{\left (50 x A -125 y \left (x \right ) A -12\right )^{2}}\right )}^{\frac {1}{6}} A y \left (x \right ) \sqrt {-25 x A +6}-\frac {4 \left (x A -\frac {5 y \left (x \right ) A}{2}-\frac {6}{25}\right ) \left (\int _{}^{\frac {2 \left (-25 x A +6\right )^{\frac {3}{2}}}{-50 x A +125 y \left (x \right ) A +12}}\frac {\left (\textit {\_a}^{2}-6\right )^{\frac {1}{6}}}{\textit {\_a}^{\frac {1}{3}}}d \textit {\_a} +c_{1} \right ) \left (\frac {\left (-25 x A +6\right )^{\frac {3}{2}}}{-50 x A +125 y \left (x \right ) A +12}\right )^{\frac {1}{3}}}{5}\right )}{\left (\frac {\left (-25 x A +6\right )^{\frac {3}{2}}}{-50 x A +125 y \left (x \right ) A +12}\right )^{\frac {1}{3}} \left (100 x A -250 y \left (x \right ) A -24\right )} = 0 \]

Problem 10695

ODE	\[ \boxed {y y^{\prime }-y=12 x +\frac {A}{x^{\frac {5}{2}}}} \]
program solution
Maple solution	\[ c_{1} +\frac {12 \sqrt {3}\, \left (2^{\frac {2}{3}} \left (\frac {3 y \left (x \right )^{2} x^{\frac {3}{2}}}{4}-6 y \left (x \right ) x^{\frac {5}{2}}+A +12 x^{\frac {7}{2}}\right ) \left (\frac {48 x^{\frac {7}{2}}-24 y \left (x \right ) x^{\frac {5}{2}}+3 y \left (x \right )^{2} x^{\frac {3}{2}}+4 A}{A}\right )^{\frac {1}{6}}-56 \operatorname {hypergeom}\left (\left [-\frac {1}{6}, \frac {1}{2}\right ], \left [\frac {3}{2}\right ], -\frac {3 x^{\frac {3}{2}} \left (-4 x +y \left (x \right )\right )^{2}}{4 A}\right ) \left (x -\frac {y \left (x \right )}{4}\right ) x^{\frac {5}{2}}\right )}{\sqrt {-A \,x^{\frac {7}{2}}}} = 0 \]

Problem 10696

ODE	\[ \boxed {y y^{\prime }-y=\frac {63 x}{4}+\frac {A}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10697

ODE	\[ \boxed {y y^{\prime }-y=2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ c_{1} -\frac {\left (3 A +\sqrt {x}\right ) 2^{\frac {1}{3}} \left (\frac {12 A^{2}+10 A \sqrt {x}+2 x -y \left (x \right )}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}\right )^{\frac {1}{3}} \left (\frac {15 A^{2}+8 A \sqrt {x}+x +y \left (x \right )}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}\right )^{\frac {1}{6}} y \left (x \right )}{4 \sqrt {\frac {\left (3 A +\sqrt {x}\right )^{2}}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}}\, \left (6 A^{2}+2 A \sqrt {x}+y \left (x \right )\right ) A}-\left (\int _{}^{\frac {6 A \sqrt {x}+2 x -3 y \left (x \right )}{12 A^{2}+4 A \sqrt {x}+2 y \left (x \right )}}\frac {\left (\textit {\_a} +1\right )^{\frac {1}{3}} \left (2 \textit {\_a} +5\right )^{\frac {1}{6}}}{\sqrt {2 \textit {\_a} +3}}d \textit {\_a} \right ) = 0 \]

Problem 10698

ODE	\[ \boxed {y y^{\prime }-y=2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right )} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10699

ODE	\[ \boxed {y y^{\prime }-y=-\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10700

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]