2.17.38 Problems 3701 to 3800

Problem 3701

ODE	\[ \boxed {\left (2+2 x -y\right ) y^{\prime }-3 y=-3-6 x} \]
program solution	\[ y = 2 x -\frac {3 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{3}+\frac {7}{3}-\frac {25 c_{1}}{3}}}{3}\right )}{5}+\frac {7}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 x -\frac {3 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {25 x}{3}+\frac {7}{3}}}{3}\right )}{5}+\frac {7}{5} \]

Problem 3702

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

Problem 3703

ODE	\[ \boxed {\left (4+2 x -y\right ) y^{\prime }-2 y=-x -5} \]
program solution	\[ \frac {3 \ln \left (y+x -1\right )}{2}-\frac {\ln \left (y-3-x \right )}{2} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\frac {1}{2}+\frac {\left (1-i \sqrt {3}\right ) \left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}\right )^{\frac {2}{3}}}{6}+\frac {i \sqrt {3}}{2}-\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} x +27 c_{1} \right )^{\frac {1}{3}} \left (x -1\right ) c_{1}}{\left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}\right )^{\frac {1}{3}} c_{1}} \]

Problem 3704

ODE	\[ \boxed {\left (5-2 x -y\right ) y^{\prime }-2 y=x -4} \]
program solution	\[ -\frac {x \left (x +4 y-8\right )}{2}+5 y-\frac {y^{2}}{2} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {3 \left (-2+x \right )^{2} c_{1}^{2}+1}+\left (-2 x +5\right ) c_{1}}{c_{1}} \]

Problem 3705

ODE	\[ \boxed {\left (1-3 x +y\right ) y^{\prime }+2 y=2 x} \]
program solution	\[ \frac {\ln \left (2 y-4 x +1\right )}{6}-\frac {2 \ln \left (y+x -1\right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{2}+\frac {\left (2 x -1\right ) \left (-1-\operatorname {RootOf}\left (-3+\left (8 c_{1} x^{3}-12 c_{1} x^{2}+6 c_{1} x -c_{1} \right ) \textit {\_Z}^{4}-\textit {\_Z} \right )\right )}{2} \]

Problem 3706

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

Problem 3707

ODE	\[ \boxed {\left (-y+4 x \right ) y^{\prime }-5 y=-2 x} \]
program solution	\[ 2 \ln \left (2 x +y\right )-\ln \left (-x +y\right ) = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {-4 c_{1} x -\sqrt {-12 c_{1} x +1}+1}{2 c_{1}} \\ y \left (x \right ) &= \frac {-4 c_{1} x +1+\sqrt {-12 c_{1} x +1}}{2 c_{1}} \\ \end{align*}

Problem 3708

ODE	\[ \boxed {\left (6-4 x -y\right ) y^{\prime }+y=2 x} \]
program solution	\[ 3 \ln \left (-3+x +y\right )-2 \ln \left (y-4+2 x \right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {2}{3}}}{12}-\left (\frac {1}{3}+\left (x -3\right ) c_{1} \right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {1}{3}}+2 \left (-1-i \sqrt {3}\right ) \left (-\frac {1}{6}+c_{1} \left (x -1\right )\right )}{\left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {1}{3}} c_{1}} \]

Problem 3709

ODE	\[ \boxed {\left (1+5 x -y\right ) y^{\prime }-5 y=-x -5} \]
program solution	\[ -2 \ln \left (-x +y-1\right )+3 \ln \left (y+x -1\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {i \left (1-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {2}{3}}+12 c_{1} x \right ) \sqrt {3}+6 \left (\left (2-{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}\right ) x +{\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}\right ) c_{1} +{\left ({\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}-1\right )}^{2}}{6 c_{1} {\left (6 \sqrt {3}\, x \sqrt {\frac {27 c_{1} x^{2}+2 x}{c_{1}}}\, c_{1}^{2}+54 c_{1}^{2} x^{2}+18 c_{1} x +1\right )}^{\frac {1}{3}}} \]

Problem 3710

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

Problem 3711

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

Problem 3712

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

Problem 3713

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

Problem 3714

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

Problem 3715

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

Problem 3716

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

Problem 3717

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

Problem 3718

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

Problem 3719

ODE	\[ \boxed {\left (1+x -2 y\right ) y^{\prime }+y=2 x +1} \]
program solution	\[ -x \left (x -y+1\right )-y^{2}+y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {4-27 \left (x +\frac {1}{3}\right )^{2} c_{1}^{2}}+\left (3 x +3\right ) c_{1}}{6 c_{1}} \]

Problem 3720

ODE	\[ \boxed {\left (1+x +2 y\right ) y^{\prime }-2 y=x -1} \]
program solution	\[ y = -\frac {x}{2}+\frac {2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {9 x}{4}-\frac {1}{4}+\frac {9 c_{1}}{2}}}{4}\right )}{3}+\frac {1}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x}{2}+\frac {2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{\frac {9 x}{4}-\frac {1}{4}}}{4}\right )}{3}+\frac {1}{6} \]

Problem 3721

ODE	\[ \boxed {\left (1+x +2 y\right ) y^{\prime }-4 y=-x -7} \]
program solution	\[ -2 \ln \left (-5-x +2 y\right )+3 \ln \left (y-4-x \right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {4 \left (\left (\frac {i \sqrt {3}}{48}-\frac {1}{48}\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{\frac {2}{3}}+\left (\frac {1}{3}+\left (-\frac {x}{4}-1\right ) c_{1} \right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{\frac {1}{3}}+\left (1+i \sqrt {3}\right ) \left (-\frac {4}{3}+\left (x +3\right ) c_{1} \right )\right )}{\left (12 \sqrt {3}\, c_{1}^{2} \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_{1} -32 x -96}{c_{1}}}+512+108 \left (x +3\right )^{2} c_{1}^{2}+\left (-576 x -1728\right ) c_{1} \right )^{\frac {1}{3}} c_{1}} \]

Problem 3722

ODE	\[ \boxed {2 \left (x +y\right ) y^{\prime }+2 y=-x^{2}} \]
program solution	\[ \frac {x^{3}}{3}+2 y x +y^{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -x -\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ y \left (x \right ) &= -x +\frac {\sqrt {-3 x^{3}+9 x^{2}-9 c_{1}}}{3} \\ \end{align*}

Problem 3723

ODE	\[ \boxed {\left (3+2 x -2 y\right ) y^{\prime }+2 y=1+6 x} \]
program solution	\[ -x \left (3 x -2 y+1\right )-y^{2}+3 y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {1-8 \left (x -\frac {1}{2}\right )^{2} c_{1}^{2}}+\left (3+2 x \right ) c_{1}}{2 c_{1}} \]

Problem 3724

ODE	\[ \boxed {\left (1-4 x -2 y\right ) y^{\prime }+y=-2 x} \]
program solution	\[ y = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-25 x +4+25 c_{1}}\right )-25 x +4+25 c_{1}}}{5}-2 x +\frac {2}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4-25 x +25 c_{1}}\right )}{10}+\frac {2}{5}-2 x \]

Problem 3725

ODE	\[ \boxed {\left (6 x -2 y\right ) y^{\prime }+y=2+3 x} \]
program solution	\[ y = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{2}\right )+\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{5}+3 x -\frac {2}{5} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{2}\right )}{5}+3 x -\frac {2}{5} \]

Problem 3726

ODE	\[ \boxed {\left (19+9 x +2 y\right ) y^{\prime }-6 y=-18+2 x} \]
program solution	\[ \frac {2 \ln \left (2 y-11-x \right )}{19}-\frac {\ln \left (2 x +2+y\right )}{19} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {1+\left (-40 x -120\right ) c_{1}}-1+\left (4 x +44\right ) c_{1}}{8 c_{1}} \]

Problem 3727

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

Problem 3728

ODE	\[ \boxed {\left (\sec \left (x \right ) \tan \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right )=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 3729

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

Problem 3730

ODE	\[ \boxed {3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}=0} \]
program solution	\[ -\ln \left (\sin \left (x \right )\right )-\frac {3 y}{10 \cos \left (y\right )^{2}}+\frac {3 \tan \left (y\right )}{10} = c_{1} \] Verified OK.
Maple solution	\[ \ln \left (\sin \left (x \right )\right )+c_{1} -\frac {3 \tan \left (y \left (x \right )\right )}{10}+\frac {3 \sec \left (y \left (x \right )\right )^{2} y \left (x \right )}{10} = 0 \]

Problem 3731

ODE	\[ \boxed {3 \left (2-y\right ) y^{\prime }+y x=0} \]
program solution	\[ y = {\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {c_{1}}{6}}}{2}\right )-\frac {x^{2}}{12}-\frac {c_{1}}{6}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {x^{2}}{12}-\frac {c_{1}}{6}}}{2}\right ) \]

Problem 3732

ODE	\[ \boxed {\left (-3 y+x \right ) y^{\prime }-y=-4-3 x} \]
program solution	\[ \frac {\ln \left (-x +y-1\right )}{6}+\frac {\ln \left (2+x +y\right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {i \left (-36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}+\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+2916 c_{1} \right )^{\frac {4}{3}}\right ) \sqrt {3}+36864 \left (x +\frac {3}{2}\right )^{6} c_{1}^{2}-48 \left (12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )^{\frac {2}{3}} \left (x +3\right ) \left (3+2 x \right )^{2} c_{1} +\left (864 c_{1} x^{3}+3888 c_{1} x^{2}+5832 c_{1} x +12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+2916 c_{1} \right )^{\frac {4}{3}}}{144 \left (12 \sqrt {3}\, \sqrt {-16384 c_{1}^{2} \left (x +\frac {3}{2}\right )^{6} \left (-\frac {27}{256}+\left (x +\frac {3}{2}\right )^{3} c_{1} \right )}+864 \left (x +\frac {3}{2}\right )^{3} c_{1} \right )^{\frac {2}{3}} c_{1} \left (3+2 x \right )^{2}} \]

Problem 3733

ODE	\[ \boxed {\left (4-x -3 y\right ) y^{\prime }-3 y=x -3} \]
program solution	\[ y = -\frac {\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {5}{3}+\frac {4 x}{3}+4 c_{1}}}{3}\right )}{2}+\frac {5}{6}-\frac {x}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x}{3}-\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {4 x}{3}+\frac {5}{3}}}{3}\right )}{2}+\frac {5}{6} \]

Problem 3734

ODE	\[ \boxed {\left (2+2 x +3 y\right ) y^{\prime }+3 y=1-2 x} \]
program solution	\[ y = 3 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {x}{9}-\frac {c_{1}}{6}-\frac {7}{9}}}{9}\right )-\frac {2 x}{3}+\frac {7}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{9}-\frac {7}{9}}}{9}\right )+\frac {7}{3} \]

Problem 3735

ODE	\[ \boxed {\left (5-2 x -3 y\right ) y^{\prime }-3 y=-1+2 x} \]
program solution	\[ y = -4 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x}{12}+\frac {c_{1}}{8}-\frac {7}{12}}}{12}\right )-\frac {2 x}{3}-\frac {7}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {2 x}{3}-4 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {x}{12}-\frac {7}{12}}}{12}\right )-\frac {7}{3} \]

Problem 3736

ODE	\[ \boxed {\left (1+9 x -3 y\right ) y^{\prime }-y=-2-3 x} \]
program solution	\[ y = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (3 \,{\mathrm e}^{-3-20 x +20 c_{1}}\right )-3-20 x +20 c_{1}}}{2}+\frac {1}{2}+3 x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (3 \,{\mathrm e}^{-20 x -3+20 c_{1}}\right )}{6}+3 x +\frac {1}{2} \]

Problem 3737

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

Problem 3738

ODE	\[ \boxed {\left (3+2 x +4 y\right ) y^{\prime }-2 y=x +1} \]
program solution	\[ y = \frac {\operatorname {LambertW}\left ({\mathrm e}^{8 x +5+16 c_{1}}\right )}{8}-\frac {x}{2}-\frac {5}{8} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]

Problem 3739

ODE	\[ \boxed {\left (5+2 x -4 y\right ) y^{\prime }+2 y=x +3} \]
program solution	\[ -\frac {x \left (6+x -4 y\right )}{2}-2 y^{2}+5 y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {x}{2}+\frac {5}{4}-\frac {\sqrt {4 c_{1} -4 x +25}}{4} \\ y \left (x \right ) &= \frac {x}{2}+\frac {5}{4}+\frac {\sqrt {4 c_{1} -4 x +25}}{4} \\ \end{align*}

Problem 3740

ODE	\[ \boxed {\left (5+3 x -4 y\right ) y^{\prime }+3 y=2+7 x} \]
program solution	\[ -\frac {x \left (4+7 x -6 y\right )}{2}-2 y^{2}+5 y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {4-6859 \left (x -\frac {7}{19}\right )^{2} c_{1}^{2}}+\left (57 x +95\right ) c_{1}}{76 c_{1}} \]

Problem 3741

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

Problem 3742

ODE	\[ \boxed {\left (11-11 x -4 y\right ) y^{\prime }+25 y=62-8 x} \]
program solution	\[ -\frac {2 \ln \left (2 y-5+x \right )}{279}+\frac {2 \ln \left (y-2-4 x \right )}{93} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {4 \left (x +\frac {1}{2}\right ) \left (i \sqrt {3}-1\right ) {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{\frac {2}{3}}+\left (-76 x +28\right ) {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{\frac {1}{3}}-64 \left (1+i \sqrt {3}\right ) \left (x +\frac {1}{2}\right )}{i \sqrt {3}\, {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{\frac {2}{3}}-16 i \sqrt {3}-{\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{\frac {2}{3}}+8 {\left (708588 \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1} \right ) c_{1} \left (x -\frac {1}{9}\right )^{2}}[phone] \left (x -\frac {1}{9}\right )^{2} c_{1} \right )}^{\frac {1}{3}}-16} \]

Problem 3743

ODE	\[ \boxed {\left (6+3 x +5 y\right ) y^{\prime }-7 y=x +2} \]
program solution	\[ -\frac {\ln \left (x +5 y+2\right )}{3}+\frac {4 \ln \left (-x +y-2\right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (-2-x \right ) {\operatorname {RootOf}\left (6+\left (c_{1} x^{3}+6 c_{1} x^{2}+12 c_{1} x +8 c_{1} \right ) \textit {\_Z}^{12}-5 \textit {\_Z}^{3}\right )}^{3}+2+x \]

Problem 3744

ODE	\[ \boxed {\left (7 x +5 y\right ) y^{\prime }+8 y=-10 x} \]
program solution	\[ \frac {3 \ln \left (2 x +y\right )}{5}+\frac {2 \ln \left (x +y\right )}{5} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \left (\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} x^{5}-2 \textit {\_Z}^{20} c_{1} x^{5}+\textit {\_Z}^{15} c_{1} x^{5}-1\right )^{5}-2\right ) \]

Problem 3745

ODE	\[ \boxed {\left (x +4 x^{3}+5 y\right ) y^{\prime }+3 y x^{2}+4 y=-7 x^{3}} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {16 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{20}+224 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{15}+784 \left (x^{15}-5 x^{13}+10 x^{11}-10 x^{9}+5 x^{7}-x^{5}+72 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{10}+2744 \left (-x^{15}+5 x^{13}-10 x^{11}+10 x^{9}-5 x^{7}+x^{5}+48 c_{1} \right ) {\operatorname {RootOf}\left (\left (-2 x^{15}+10 x^{13}-20 x^{11}+20 x^{9}-10 x^{7}+2 x^{5}+96 c_{1} \right ) \textit {\_Z}^{25}+\left (-35 x^{15}+175 x^{13}-350 x^{11}+350 x^{9}-175 x^{7}+35 x^{5}+1680 c_{1} \right ) \textit {\_Z}^{20}+11760 c_{1} \textit {\_Z}^{15}+41160 c_{1} \textit {\_Z}^{10}+72030 c_{1} \textit {\_Z}^{5}+50421 c_{1} \right )}^{5}-12005 x^{13}+48020 x^{11}-72030 x^{9}+48020 x^{7}-12005 x^{5}+115248 c_{1}}{12005 x^{4} \left (x -1\right )^{4} \left (x +1\right )^{4}} \]

Problem 3746

ODE	\[ \boxed {\left (5-x +6 y\right ) y^{\prime }-4 y=3-x} \]
program solution	\[ 2 \ln \left (2 y+1-x \right )-\ln \left (-x +2+3 y\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {9+\left (-8 x -8\right ) c_{1}}-3+\left (4 x -4\right ) c_{1}}{8 c_{1}} \]

Problem 3747

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

Problem 3748

ODE	\[ \boxed {\left (3-3 x +7 y\right ) y^{\prime }+3 y=-7+7 x} \]
program solution	\[ \frac {2 \ln \left (-x +1+y\right )}{3}+\frac {5 \ln \left (y+x -1\right )}{3} = c_{1} \] Verified OK.
Maple solution	\[ \text {Expression too large to display} \]

Problem 3749

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

Problem 3750

ODE	\[ \boxed {\left (8+5 x -12 y\right ) y^{\prime }+5 y=3+2 x} \]
program solution	\[ -x \left (x -5 y+3\right )-6 y^{2}+8 y = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {-\sqrt {\left (x +4\right )^{2} c_{1}^{2}+24}+\left (5 x +8\right ) c_{1}}{12 c_{1}} \]

Problem 3751

ODE	\[ \boxed {\left (140+7 x -16 y\right ) y^{\prime }+y=-25-8 x} \]
program solution	\[ \frac {5 \ln \left (x +2 y-10\right )}{8}+\frac {3 \ln \left (-x +y-11\right )}{8} = c_{1} \] Verified OK.
Maple solution	\[ \text {Expression too large to display} \]

Problem 3752

ODE	\[ \boxed {\left (3+9 x +21 y\right ) y^{\prime }+5 y=45+7 x} \]
program solution	\[ \frac {3 \ln \left (x +3+y\right )}{7}+\frac {4 \ln \left (3 y-x -11\right )}{7} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-x -5\right ) {\operatorname {RootOf}\left (-27+\left (c_{1} x^{7}+35 c_{1} x^{6}+525 c_{1} x^{5}+4375 c_{1} x^{4}+21875 c_{1} x^{3}+65625 c_{1} x^{2}+109375 c_{1} x +78125 c_{1} \right ) \textit {\_Z}^{49}+\left (-12 c_{1} x^{7}-420 c_{1} x^{6}-6300 c_{1} x^{5}-52500 c_{1} x^{4}-262500 c_{1} x^{3}-787500 c_{1} x^{2}-1312500 c_{1} x -937500 c_{1} \right ) \textit {\_Z}^{42}+\left (48 c_{1} x^{7}+1680 c_{1} x^{6}+25200 c_{1} x^{5}+210000 c_{1} x^{4}+1050000 c_{1} x^{3}+3150000 c_{1} x^{2}+5250000 c_{1} x +3750000 c_{1} \right ) \textit {\_Z}^{35}+\left (-64 c_{1} x^{7}-2240 c_{1} x^{6}-33600 c_{1} x^{5}-280000 c_{1} x^{4}-1400000 c_{1} x^{3}-4200000 c_{1} x^{2}-7000000 c_{1} x -5000000 c_{1} \right ) \textit {\_Z}^{28}\right )}^{7}}{3}+\frac {11}{3}+\frac {x}{3} \]

Problem 3753

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

Problem 3754

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

Problem 3755

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

Problem 3756

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

Problem 3757

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

Problem 3758

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

Problem 3759

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

Problem 3760

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

Problem 3761

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

Problem 3762

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

Problem 3763

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

Problem 3764

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

Problem 3765

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

Problem 3766

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

Problem 3767

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

Problem 3768

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

Problem 3769

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

Problem 3770

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

Problem 3771

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

Problem 3772

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

Problem 3773

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

Problem 3774

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

Problem 3775

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

Problem 3776

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

Problem 3777

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

Problem 3778

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

Problem 3779

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

Problem 3780

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

Problem 3781

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

Problem 3782

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

Problem 3783

ODE	\[ \boxed {\left (a +x \left (x +y\right )\right ) y^{\prime }-b \left (x +y\right ) y=0} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 3784

ODE	\[ \boxed {x \left (2 x +y\right ) y^{\prime }-y x +y^{2}=x^{2}} \]
program solution	\[ -\frac {\ln \left (x +y\right )}{3}+\frac {5 \ln \left (-x +2 y\right )}{6} = -\frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x \left (\operatorname {RootOf}\left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 c_{1} x^{3}\right )^{9}+c_{1} x^{3}\right )}{-\operatorname {RootOf}\left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 c_{1} x^{3}\right )^{9}+2 c_{1} x^{3}} \]

Problem 3785

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

Problem 3786

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

Problem 3787

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

Problem 3788

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

Problem 3789

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

Problem 3790

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

Problem 3791

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

Problem 3792

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

Problem 3793

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

Problem 3794

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

Problem 3795

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

Problem 3796

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

Problem 3797

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

Problem 3798

ODE	\[ \boxed {\left (3-x +2 y x \right ) y^{\prime }-y+y^{2}=-3 x^{2}} \]
program solution	\[ x \left (x^{2}+y^{2}-y\right )+3 y = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {x -3+\sqrt {9-4 x^{4}+x^{2}+\left (-4 c_{1} -6\right ) x}}{2 x} \\ y \left (x \right ) &= \frac {x -3-\sqrt {9-4 x^{4}+x^{2}+\left (-4 c_{1} -6\right ) x}}{2 x} \\ \end{align*}

Problem 3799

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

Problem 3800

ODE	\[ \boxed {x \left (2 y+x \right ) y^{\prime }+\left (2 x -y\right ) y=0} \]
program solution	\[ \frac {\ln \left (y\right )}{3}+\frac {5 \ln \left (3 x +y\right )}{3} = \ln \left (x \right )+c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{18}+3 \textit {\_Z}^{3} c_{1} x^{3}-c_{1} x^{3}\right )^{15}}{c_{1} x^{2}} \]