2.17.31 Problems 3001 to 3100

Problem 3001

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

Problem 3002

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

Problem 3003

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

Problem 3004

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

Problem 3005

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

Problem 3006

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

Problem 3007

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

Problem 3008

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

Problem 3009

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

Problem 3010

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

Problem 3011

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

Problem 3012

ODE	\[ \boxed {y^{\prime }-y \tan \left (x \right )=x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ y = \tan \left (x \right ) x +1-\sec \left (x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 1+\tan \left (x \right ) x -\sec \left (x \right ) \]

Problem 3013

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

Problem 3014

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

Problem 3015

ODE	\[ \boxed {y^{\prime } x -y=x} \] With initial conditions \begin {align*} [y \left (-1\right ) = -1] \end {align*}
program solution	\[ y = -i \pi x +\ln \left (x \right ) x +x \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (\ln \left (x \right )+1-i \pi \right ) x \]

Problem 3016

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

Problem 3017

ODE	\[ \boxed {y^{\prime }={\mathrm e}^{x} \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {{\mathrm e}^{x} \sin \left (x \right )}{2}-\frac {\cos \left (x \right ) {\mathrm e}^{x}}{2}+\frac {1}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {1}{2}+\frac {{\mathrm e}^{x} \left (\sin \left (x \right )-\cos \left (x \right )\right )}{2} \]

Problem 3018

ODE	\[ \boxed {y^{\prime }-3 y={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}} \] With initial conditions \begin {align*} [y \left (5\right ) = 5] \end {align*}
program solution	\[ y = x \,{\mathrm e}^{3 x}-5 \,{\mathrm e}^{3 x}+\frac {{\mathrm e}^{3 x -30}}{6}+5 \,{\mathrm e}^{3 x -15}-\frac {{\mathrm e}^{-3 x}}{6} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{3 x -30}}{6}+5 \,{\mathrm e}^{3 x -15}+\left (x -5\right ) {\mathrm e}^{3 x}-\frac {{\mathrm e}^{-3 x}}{6} \]

Problem 3019

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

Problem 3020

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

Problem 3021

ODE	\[ \boxed {2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right )=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{12}\right ) = \frac {\pi }{8}\right ] \end {align*}
program solution	\[ -\frac {\ln \left (\sin \left (3 x \right )\right )}{3}+\frac {\ln \left (\sec \left (2 y\right )^{2}\right )}{6} = \frac {\ln \left (2\right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\pi }{4}-\frac {\arctan \left (\frac {1}{\sqrt {1-2 \cos \left (6 x \right )}}\right )}{2} \]

Problem 3022

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

Problem 3023

ODE	\[ \boxed {y^{\prime }-\frac {2 x -y}{y+2 x}=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 2] \end {align*}
program solution	\[ \frac {\ln \left (y^{2}+3 y x -2 x^{2}\right )}{2}-\frac {\sqrt {17}\, \operatorname {arctanh}\left (\frac {\left (2 y+3 x \right ) \sqrt {17}}{17 x}\right )}{17} = \frac {3 \ln \left (2\right )}{2}-\frac {\sqrt {17}\, \operatorname {arccoth}\left (\frac {5 \sqrt {17}}{17}\right )}{17}+\frac {i \sqrt {17}\, \pi }{34} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (-2 \sqrt {17}\, \operatorname {arctanh}\left (\frac {5 \sqrt {17}}{17}\right )+2 \sqrt {17}\, \operatorname {arctanh}\left (\frac {\left (3 x +2 \textit {\_Z} \right ) \sqrt {17}}{17 x}\right )+51 \ln \left (2\right )-34 \ln \left (x \right )-17 \ln \left (\frac {\textit {\_Z}^{2}+3 x \textit {\_Z} -2 x^{2}}{x^{2}}\right )\right ) \]

Problem 3024

ODE	\[ \boxed {y^{\prime }-\frac {3 x -y+1}{3 y-x +5}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ \frac {\ln \left (y+1-x \right )}{3}+\frac {2 \ln \left (y+3+x \right )}{3} = \frac {2 \ln \left (3\right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {4}{3}}-12 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}} x -84 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}+576 x^{2}+1152 x +576}{36 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}} \]

Problem 3025

ODE	\[ \boxed {3 y+\left (7 y-3 x +3\right ) y^{\prime }=7 x -7} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ \frac {2 \ln \left (y+1-x \right )}{3}+\frac {5 \ln \left (y+x -1\right )}{3} = \frac {5 i \pi }{3} \] Verified OK.
Maple solution	\[ \text {Expression too large to display} \]

Problem 3026

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

Problem 3027

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

Problem 3028

ODE	\[ \boxed {\left (x +y^{2}\right ) y^{\prime }+y=x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
program solution	\[ -\frac {x^{3}}{3}+y x +\frac {y^{3}}{3} = 1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{\frac {2}{3}}-4 x}{2 \left (12+4 x^{3}+4 \sqrt {x^{6}+10 x^{3}+9}\right )^{\frac {1}{3}}} \]

Problem 3029

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 3030

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

Problem 3031

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

Problem 3032

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

Problem 3033

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

Problem 3034

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

Problem 3035

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

Problem 3036

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

Problem 3037

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

Problem 3038

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

Problem 3039

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

Problem 3040

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

Problem 3041

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

Problem 3042

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

Problem 3043

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

Problem 3044

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

Problem 3045

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

Problem 3046

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

Problem 3047

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

Problem 3048

ODE	\[ \boxed {\sqrt {x^{2}+1}\, y^{\prime }+y=2 x} \]
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 3049

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

Problem 3050

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

Problem 3051

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

Problem 3052

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

Problem 3053

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

Problem 3054

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

Problem 3055

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

Problem 3056

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

Problem 3057

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

Problem 3058

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

Problem 3059

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

Problem 3060

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

Problem 3061

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

Problem 3062

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

Problem 3063

ODE	\[ \boxed {y^{\prime }+2 y x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5] \end {align*}
program solution	\[ y = 5 \,{\mathrm e}^{-x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 5 \,{\mathrm e}^{-x^{2}} \]

Problem 3064

ODE	\[ \boxed {\cot \left (x \right ) y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
program solution	\[ y = \frac {2}{\cos \left (x \right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \sec \left (x \right ) \]

Problem 3065

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

Problem 3066

ODE	\[ \boxed {-2 y x +y^{\prime }=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{x^{2}}-1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \,{\mathrm e}^{x^{2}}-1 \]

Problem 3067

ODE	\[ \boxed {y^{\prime } x -y x -y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
program solution	\[ y = x \,{\mathrm e}^{x -1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x \,{\mathrm e}^{x -1} \]

Problem 3068

ODE	\[ \boxed {\left (x^{3}+1\right ) y^{\prime }=3 \tan \left (x \right ) x^{2}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = \frac {\pi }{2}\right ] \end {align*}
program solution	\[ y = \int _{0}^{x}\frac {3 \tan \left (\textit {\_a} \right ) \textit {\_a}^{2}}{\textit {\_a}^{3}+1}d \textit {\_a} +\frac {\pi }{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \left (\int _{0}^{x}\frac {\tan \left (\textit {\_z1} \right ) \textit {\_z1}^{2}}{\left (\textit {\_z1} +1\right ) \left (\textit {\_z1}^{2}-\textit {\_z1} +1\right )}d \textit {\_z1} \right )+\frac {\pi }{2} \]

Problem 3069

ODE	\[ \boxed {x \cos \left (y\right ) y^{\prime }-\sin \left (y\right )=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
program solution	\[ -\ln \left (x \right )+\ln \left (1+\sin \left (y\right )\right ) = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arcsin \left (x -1\right ) \]

Problem 3070

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

Problem 3071

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

Problem 3072

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

Problem 3073

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

Problem 3074

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

Problem 3075

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

Problem 3076

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

Problem 3077

ODE	\[ \boxed {y^{\prime } x y-\sqrt {y^{2}-9}=0} \] With initial conditions \begin {align*} [y \left ({\mathrm e}^{4}\right ) = 5] \end {align*}
program solution	\[ -\ln \left (x \right )+\frac {\left (y-3\right ) \left (y+3\right )}{\sqrt {y^{2}-9}} = 0 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {9+\ln \left (x \right )^{2}} \]

Problem 3078

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

Problem 3079

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

Problem 3080

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

Problem 3081

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

Problem 3082

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

Problem 3083

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

Problem 3084

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

Problem 3085

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

Problem 3086

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

Problem 3087

ODE	\[ \boxed {y^{\prime }-\frac {x +y+4}{x -y-6}=0} \]
program solution	\[ \frac {\ln \left (y^{2}+x^{2}+10 y-2 x +26\right )}{2}-\arctan \left (\frac {y+5}{x -1}\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -5-\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]

Problem 3088

ODE	\[ \boxed {y^{\prime }-\frac {x +y+4}{x +y-6}=0} \]
program solution	\[ y = -5 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {2 x}{5}-\frac {2 c_{1}}{5}+\frac {1}{5}}}{5}\right )-x +1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -x -5 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{-\frac {2 x}{5}+\frac {1}{5}}}{5}\right )+1 \]

Problem 3089

ODE	\[ \boxed {\left (x +\frac {2}{y}\right ) y^{\prime }+y=0} \]
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	\[ y \left (x \right ) = \frac {2 \operatorname {LambertW}\left (\frac {x \,{\mathrm e}^{\frac {c_{1}}{2}}}{2}\right )}{x} \]

Problem 3090

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

Problem 3091

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

Problem 3092

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

Problem 3093

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

Problem 3094

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

Problem 3095

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

Problem 3096

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

Problem 3097

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

Problem 3098

ODE	\[ \boxed {2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime }=0} \]
program solution	\[ y \left (x^{2} y^{2}+\sin \left (x \right )\right ) = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {2}{3}}-12 \sin \left (x \right )}{6 x \left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {i \sqrt {3}\, \left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {2}{3}}+12 i \sqrt {3}\, \sin \left (x \right )+\left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {2}{3}}-12 \sin \left (x \right )}{12 x \left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {i \sqrt {3}\, \left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {2}{3}}+12 i \sqrt {3}\, \sin \left (x \right )-\left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {2}{3}}+12 \sin \left (x \right )}{12 x \left (12 \sqrt {3}\, \sqrt {27 c_{1}^{2} x^{2}+4 \sin \left (x \right )^{3}}-108 c_{1} x \right )^{\frac {1}{3}}} \\ \end{align*}

Problem 3099

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

Problem 3100

ODE	\[ \boxed {\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x=0} \]
program solution	\[ -\frac {x^{2}}{y^{3}}+\frac {1}{y} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {1+\frac {\left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}}}{2}+\frac {2}{\left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}}}}{3 c_{1}} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {2}{3}}-4 i \sqrt {3}-4 \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}}+4}{12 \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}} c_{1}} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {2}{3}}-4 i \sqrt {3}+4 \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}}-4}{12 \left (12 \sqrt {3}\, x \sqrt {27 c_{1}^{2} x^{2}-4}\, c_{1} -108 c_{1}^{2} x^{2}+8\right )^{\frac {1}{3}} c_{1}} \\ \end{align*}