2.17.37 Problems 3601 to 3700

Problem 3601

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

Problem 3602

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

Problem 3603

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

Problem 3604

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

Problem 3605

ODE	\[ \boxed {y^{\prime } x^{3}+x^{2} y \left (1-y x^{2}\right )=-20} \]
program solution	\[ y = \frac {-5 c_{3} x^{9}+4}{x^{2} \left (c_{3} x^{9}+1\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {5 x^{9}+4 c_{1}}{\left (-x^{9}+c_{1} \right ) x^{2}} \]

Problem 3606

ODE	\[ \boxed {y^{\prime } x^{3}+\left (-2 x +3\right ) x^{2} y-x^{6} y^{2}=-3} \]
program solution	\[ y = \frac {-3 c_{3} {\mathrm e}^{4 x}+1}{x^{3} \left (c_{3} {\mathrm e}^{4 x}+1\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-3 \,{\mathrm e}^{4 x} c_{1} -3}{x^{3} \left ({\mathrm e}^{4 x} c_{1} -3\right )} \]

Problem 3607

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

Problem 3608

ODE	\[ \boxed {y^{\prime } x^{3}-\cos \left (y\right ) \left (\cos \left (y\right )-2 \sin \left (y\right ) x^{2}\right )=0} \]
program solution
Maple solution	\[ y \left (x \right ) = \arctan \left (\frac {\ln \left (x \right )-c_{1}}{x^{2}}\right ) \]

Problem 3609

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

Problem 3610

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

Problem 3611

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

Problem 3612

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

Problem 3613

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

Problem 3614

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

Problem 3615

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

Problem 3616

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

Problem 3617

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

Problem 3618

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

Problem 3619

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

Problem 3620

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

Problem 3621

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

Problem 3622

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

Problem 3623

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

Problem 3624

ODE	\[ \boxed {x \left (c \,x^{2}+b x +a \right ) y^{\prime }-\left (c \,x^{2}+b x +a \right ) y-y^{2}=-x^{2}} \]
program solution	\[ y = -\frac {\left (c_{3} \cosh \left (\frac {2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right )+\sinh \left (\frac {2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right )\right ) x}{c_{3} \sinh \left (\frac {2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right )+\cosh \left (\frac {2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\tanh \left (\frac {c_{1} \sqrt {4 a c -b^{2}}+2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right ) x \]

Problem 3625

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

Problem 3626

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

Problem 3627

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

Problem 3628

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

Problem 3629

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

Problem 3630

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

Problem 3631

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

Problem 3632

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

Problem 3633

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

Problem 3634

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

Problem 3635

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

Problem 3636

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

Problem 3637

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

Problem 3638

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

Problem 3639

ODE	\[ \boxed {x^{n} y^{\prime }+y^{2}=-x^{-2+2 n}-\left (-n +1\right ) x^{n -1}} \]
program solution	\[ y = \frac {x^{n -1} \left (2 \left (n -1\right ) \left (\operatorname {BesselJ}\left (\frac {-\sqrt {n^{2}-2 n -3}+n -1}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right ) c_{3} +\operatorname {BesselY}\left (\frac {-\sqrt {n^{2}-2 n -3}+n -1}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right )\right ) x^{-\frac {n}{2}+\frac {1}{2}}+\left (\operatorname {BesselY}\left (-\frac {\sqrt {n^{2}-2 n -3}}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right )+\operatorname {BesselJ}\left (-\frac {\sqrt {n^{2}-2 n -3}}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right ) c_{3} \right ) \left (\sqrt {n^{2}-2 n -3}-n +1\right ) \sqrt {-n +1}\right )}{\sqrt {-n +1}\, \left (2 \operatorname {BesselJ}\left (-\frac {\sqrt {n^{2}-2 n -3}}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right ) c_{3} +2 \operatorname {BesselY}\left (-\frac {\sqrt {n^{2}-2 n -3}}{n -1}, \frac {2 x^{-\frac {n}{2}+\frac {1}{2}}}{\sqrt {-n +1}}\right )\right )} \] Verified OK.
Maple solution	\[ \text {Expression too large to display} \]

Problem 3640

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

Problem 3641

ODE	\[ \boxed {x^{n} y^{\prime }-x^{n -1} \left (a \,x^{2 n}+y n -b y^{2}\right )=0} \]
program solution	\[ y = \frac {x^{n} \sqrt {-a b}\, \left (c_{3} \cos \left (\frac {x^{n} \sqrt {-a b}}{n}\right )-\sin \left (\frac {x^{n} \sqrt {-a b}}{n}\right )\right )}{b \left (c_{3} \sin \left (\frac {x^{n} \sqrt {-a b}}{n}\right )+\cos \left (\frac {x^{n} \sqrt {-a b}}{n}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\tanh \left (\frac {x^{n} \sqrt {a}\, \sqrt {b}+i c_{1} n}{n}\right ) \sqrt {a}\, x^{n}}{\sqrt {b}} \]

Problem 3642

ODE	\[ \boxed {x^{k} y^{\prime }-b y^{n}=a \,x^{m}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 3643

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

Problem 3644

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

Problem 3645

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

Problem 3646

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

Problem 3647

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

Problem 3648

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

Problem 3649

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

Problem 3650

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

Problem 3651

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

Problem 3652

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

Problem 3653

ODE	\[ \boxed {x^{\frac {3}{2}} y^{\prime }-b \,x^{\frac {3}{2}} y^{2}=a} \]
program solution	\[ y = \frac {2 a \left (\operatorname {BesselY}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right )+\operatorname {BesselJ}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) c_{3} \right )}{\sqrt {x}\, \left (2 \operatorname {BesselJ}\left (0, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) c_{3} x^{\frac {1}{4}} \sqrt {a}\, \sqrt {b}+2 \operatorname {BesselY}\left (0, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}-\operatorname {BesselJ}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) c_{3} -\operatorname {BesselY}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {2 a \left (\operatorname {BesselJ}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) c_{1} +\operatorname {BesselY}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right )\right )}{\sqrt {x}\, \left (-2 \sqrt {a}\, x^{\frac {1}{4}} \operatorname {BesselJ}\left (0, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) \sqrt {b}\, c_{1} -2 \operatorname {BesselY}\left (0, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}+\operatorname {BesselJ}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right ) c_{1} +\operatorname {BesselY}\left (1, 4 \sqrt {a}\, \sqrt {b}\, x^{\frac {1}{4}}\right )\right )} \]

Problem 3654

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

Problem 3655

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

Problem 3656

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

Problem 3657

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

Problem 3658

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

Problem 3659

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

Problem 3660

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

Problem 3661

ODE	\[ \boxed {y^{\prime } \left (x^{3}+1\right )^{\frac {2}{3}}+\left (1+y^{3}\right )^{\frac {2}{3}}=0} \]
program solution	\[ -\frac {2 x \pi \sqrt {3}\, \operatorname {LegendreP}\left (-\frac {1}{3}, -\frac {1}{3}, \frac {-x^{3}+1}{x^{3}+1}\right )}{9 \left (-x^{3}\right )^{\frac {1}{6}} \left (x^{3}+1\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )}-\operatorname {hypergeom}\left (\left [\frac {1}{3}, \frac {2}{3}\right ], \left [\frac {4}{3}\right ], -y^{3}\right ) y = c_{1} \] Verified OK.
Maple solution	\[ c_{1} +\frac {2 \pi \sqrt {3}\, \left (y \left (x \right ) \left (x^{3}+1\right )^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{6}} \operatorname {LegendreP}\left (-\frac {1}{3}, -\frac {1}{3}, \frac {-y \left (x \right )^{3}+1}{1+y \left (x \right )^{3}}\right )+\left (1+y \left (x \right )^{3}\right )^{\frac {1}{3}} \operatorname {LegendreP}\left (-\frac {1}{3}, -\frac {1}{3}, \frac {-x^{3}+1}{x^{3}+1}\right ) \left (-y \left (x \right )^{3}\right )^{\frac {1}{6}} x \right )}{9 \left (-x^{3}\right )^{\frac {1}{6}} \left (x^{3}+1\right )^{\frac {1}{3}} \left (-y \left (x \right )^{3}\right )^{\frac {1}{6}} \left (1+y \left (x \right )^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )} = 0 \]

Problem 3662

ODE	\[ \boxed {y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{\frac {2}{3}}=0} \]
program solution	\[ \int _{}^{x}-\frac {1}{\left (4 \textit {\_a}^{3}+\textit {\_a} \operatorname {a1} +\operatorname {a0} \right )^{\frac {2}{3}}}d \textit {\_a} +\int _{0}^{y}-\frac {1}{\left (4 \textit {\_a}^{3}+\textit {\_a} \operatorname {a1} +\operatorname {a0} \right )^{\frac {2}{3}}}d \textit {\_a} = c_{1} \] Verified OK.
Maple solution	\[ \int \frac {1}{\left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}}d x +\int _{}^{y \left (x \right )}\frac {1}{\left (4 \textit {\_a}^{3}+\textit {\_a} \operatorname {a1} +\operatorname {a0} \right )^{\frac {2}{3}}}d \textit {\_a} +c_{1} = 0 \]

Problem 3663

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

Problem 3664

ODE	\[ \boxed {y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )-y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )=0} \]
program solution	\[ y = \frac {\cos \left (\frac {x}{4}\right ) \cot \left (\frac {x}{2}\right ) \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )^{\frac {1}{a}} \sqrt {2}\, \sqrt {\cos \left (\frac {x}{2}\right )-1}\, \cos \left (\frac {x}{2}\right )^{\frac {-3 a -2}{a}}}{2 \left (\int \cos \left (\frac {x}{2}\right )^{\frac {-3 a -2}{a}} \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )^{\frac {-a +1}{a}} \sqrt {-\sin \left (\frac {x}{4}\right )^{2}}\, \cos \left (\frac {x}{4}\right )d x \right )+c_{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sec \left (\frac {x}{2}\right )^{2} \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )^{\frac {1}{a}} \cos \left (\frac {x}{2}\right )^{-\frac {2}{a}}}{\int \tan \left (\frac {x}{2}\right ) \sec \left (\frac {x}{2}\right )^{2} \cos \left (\frac {x}{2}\right )^{-\frac {2}{a}} \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )^{\frac {-a +1}{a}}d x +c_{1}} \]

Problem 3665

ODE	\[ \boxed {\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }-\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y=0} \]
program solution	\[ y = \frac {{\mathrm e}^{-c_{1}} \left (2 \cos \left (x \right )+1\right ) \left (2 \cos \left (x \right )-1\right )}{\cos \left (x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (4 \cos \left (x \right )-\sec \left (x \right )\right ) c_{1} \]

Problem 3666

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

Problem 3667

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

Problem 3668

ODE	\[ \boxed {\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a1} y \sin \left (2 x \right )=-\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )} \]
program solution	\[ y = -\frac {2 \sin \left (2 x \right ) \operatorname {a1} \operatorname {a2} x -2 \operatorname {a1} \operatorname {a2} \,x^{2}-4 \operatorname {a2} \operatorname {a3} \,x^{2}+\operatorname {a1} \operatorname {a2} \cos \left (2 x \right )-\operatorname {a1} \operatorname {a2} +8 c_{1}}{4 \left (\operatorname {a1} \cos \left (2 x \right )-2 \operatorname {a0} -\operatorname {a1} \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {a2} \operatorname {a1} \cos \left (2 x \right )+2 \operatorname {a2} x \operatorname {a1} \sin \left (2 x \right )-2 x^{2} \left (\operatorname {a1} +2 \operatorname {a3} \right ) \operatorname {a2} +8 c_{1}}{-4 \operatorname {a1} \cos \left (2 x \right )+8 \operatorname {a0} +4 \operatorname {a1}} \]

Problem 3669

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

Problem 3670

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

Problem 3671

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

Problem 3672

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

Problem 3673

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

Problem 3674

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

Problem 3675

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

Problem 3676

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

Problem 3677

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

Problem 3678

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

Problem 3679

ODE	\[ \boxed {y y^{\prime }-a y^{2}=b \cos \left (x +c \right )} \]
program solution	\[ \frac {\left (4 y^{2} a^{2}+4 b \cos \left (x +c \right ) a -2 b \sin \left (x +c \right )+y^{2}\right ) {\mathrm e}^{-2 x a}}{8 a^{2}+2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {16 \left (a^{2}+\frac {1}{4}\right )^{2} c_{1} {\mathrm e}^{2 a x}-16 \left (a^{2}+\frac {1}{4}\right ) b \left (a \cos \left (x +c \right )-\frac {\sin \left (x +c \right )}{2}\right )}}{4 a^{2}+1} \\ y \left (x \right ) &= -\frac {\sqrt {16 \left (a^{2}+\frac {1}{4}\right )^{2} c_{1} {\mathrm e}^{2 a x}-16 \left (a^{2}+\frac {1}{4}\right ) b \left (a \cos \left (x +c \right )-\frac {\sin \left (x +c \right )}{2}\right )}}{4 a^{2}+1} \\ \end{align*}

Problem 3680

ODE	\[ \boxed {y y^{\prime }-\operatorname {a1} y-\operatorname {a2} y^{2}=\operatorname {a0}} \]
program solution	\[ \int _{}^{y}\frac {\textit {\_a}}{\textit {\_a}^{2} \operatorname {a2} +\textit {\_a} \operatorname {a1} +\operatorname {a0}}d \textit {\_a} = x +c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {4 \tan \left (\operatorname {RootOf}\left (2 c_{1} \operatorname {a2} \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}+2 x \operatorname {a2} \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}+2 \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \ln \left (2\right )-\sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \ln \left (\frac {\sec \left (\textit {\_Z} \right )^{2} \left (4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}\right )}{\operatorname {a2}}\right )+2 \textit {\_Z} \operatorname {a1} \right )\right ) \operatorname {a0} \operatorname {a2} -\tan \left (\operatorname {RootOf}\left (2 c_{1} \operatorname {a2} \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}+2 x \operatorname {a2} \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}+2 \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \ln \left (2\right )-\sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \ln \left (\frac {\sec \left (\textit {\_Z} \right )^{2} \left (4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}\right )}{\operatorname {a2}}\right )+2 \textit {\_Z} \operatorname {a1} \right )\right ) \operatorname {a1}^{2}-\sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}\, \operatorname {a1}}{2 \operatorname {a2} \sqrt {4 \operatorname {a0} \operatorname {a2} -\operatorname {a1}^{2}}} \]

Problem 3681

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

Problem 3682

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

Problem 3683

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

Problem 3684

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

Problem 3685

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

Problem 3686

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

Problem 3687

ODE	\[ \boxed {\left (y+1\right ) y^{\prime }-\left (1-y\right ) x^{2}=0} \]
program solution	\[ y = 2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {x^{3}}{6}-\frac {c_{1}}{2}-\frac {1}{2}}}{2}\right )+1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x^{3}}{6}-\frac {1}{2}}}{2}\right )+1 \]

Problem 3688

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

Problem 3689

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

Problem 3690

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

Problem 3691

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

Problem 3692

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

Problem 3693

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

Problem 3694

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

Problem 3695

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

Problem 3696

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

Problem 3697

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

Problem 3698

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

Problem 3699

ODE	\[ \boxed {\left (3-x +y\right ) y^{\prime }-3 y=11-4 x} \]
program solution	\[ y = {\mathrm e}^{\operatorname {LambertW}\left (\left (x -2\right ) {\mathrm e}^{-c_{1}}\right )+c_{1}}-5+2 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (2 x -5\right ) \operatorname {LambertW}\left (-c_{1} \left (-2+x \right )\right )-2+x}{\operatorname {LambertW}\left (-c_{1} \left (-2+x \right )\right )} \]

Problem 3700

ODE	\[ \boxed {\left (2 x +y\right ) y^{\prime }-2 y=-x} \]
program solution	\[ \frac {\ln \left (x^{2}+y^{2}\right )}{2}-2 \arctan \left (\frac {x}{y}\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]