4.9.65 Problems 6401 to 6500

Table 4.753: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

16698

\[ {} y^{\prime }-y \,{\mathrm e}^{x} = 2 x \,{\mathrm e}^{{\mathrm e}^{x}} \]

16699

\[ {} y^{\prime }+y x \,{\mathrm e}^{x} = {\mathrm e}^{\left (1-x \right ) {\mathrm e}^{x}} \]

16700

\[ {} y^{\prime }-y \ln \left (2\right ) = 2^{\sin \left (x \right )} \left (-1+\cos \left (x \right )\right ) \ln \left (2\right ) \]

16701

\[ {} y^{\prime }-y = -2 \,{\mathrm e}^{-x} \]

16702

\[ {} \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y = -\frac {\sin \left (x \right )^{2}}{x^{2}} \]

16703

\[ {} x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right ) = -1 \]

16704

\[ {} 2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \]

16705

\[ {} y^{\prime } x^{2}+y = \left (x^{2}+1\right ) {\mathrm e}^{x} \]

16706

\[ {} x y^{\prime }+y = 2 x \]

16707

\[ {} \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 1 \]

16708

\[ {} \cos \left (x \right ) y^{\prime }-y \sin \left (x \right ) = -\sin \left (2 x \right ) \]

16709

\[ {} y^{\prime }+2 x y = 2 x y^{2} \]

16710

\[ {} 3 x y^{2} y^{\prime }-2 y^{3} = x^{3} \]

16711

\[ {} \left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime } = 3 x^{2} \]

16712

\[ {} y^{\prime }+3 x y = y \,{\mathrm e}^{x^{2}} \]

16713

\[ {} y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}} \]

16714

\[ {} 2 \ln \left (x \right ) y^{\prime }+\frac {y}{x} = \frac {\cos \left (x \right )}{y} \]

16715

\[ {} 2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = y^{3} \sin \left (x \right )^{2} \]

16716

\[ {} \left (1+x^{2}+y^{2}\right ) y^{\prime }+x y = 0 \]

16717

\[ {} y^{\prime }-\cos \left (x \right ) y = y^{2} \cos \left (x \right ) \]

16718

\[ {} y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )} \]

16719

\[ {} y^{\prime } = y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \]

16720

\[ {} \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 1+x \]

16721

\[ {} y y^{\prime }+1 = \left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \]

16722

\[ {} y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \]

16723

\[ {} x \left (2 x^{2}+y^{2}\right )+y \left (2 y^{2}+x^{2}\right ) y^{\prime } = 0 \]

16724

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

16725

\[ {} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \]

16726

\[ {} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \]

16727

\[ {} 2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \]

16728

\[ {} \frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0 \]

16729

\[ {} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \]

16730

\[ {} \frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \]

16731

\[ {} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0 \]

16732

\[ {} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0 \]

16733

\[ {} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]

16734

\[ {} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0 \]

16735

\[ {} 3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0 \]

16736

\[ {} 1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime } = 0 \]

16737

\[ {} x^{2}+y-x y^{\prime } = 0 \]

16738

\[ {} x +y^{2}-2 x y y^{\prime } = 0 \]

16739

\[ {} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime } = 0 \]

16740

\[ {} x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

16741

\[ {} x +\sin \left (x \right )+\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0 \]

16742

\[ {} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime } = 0 \]

16743

\[ {} 3 y^{2}-x +\left (2 y^{3}-6 x y\right ) y^{\prime } = 0 \]

16744

\[ {} x^{2}+y^{2}+1-2 x y y^{\prime } = 0 \]

16745

\[ {} x -x y+\left (y+x^{2}\right ) y^{\prime } = 0 \]

16777

\[ {} {\mathrm e}^{-x} y^{\prime }+y^{2}-2 y \,{\mathrm e}^{x} = 1-{\mathrm e}^{2 x} \]

16778

\[ {} y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right ) = 0 \]

16779

\[ {} x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \]

16780

\[ {} y^{\prime } x^{2} = 1+x y+x^{2} y^{2} \]

16785

\[ {} y^{\prime } = y^{{2}/{3}}+a \]

16796

\[ {} y^{\prime } = \left (x -y\right )^{2}+1 \]

16797

\[ {} x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x \]

16798

\[ {} y^{\prime }+\cos \left (x \right ) y = y^{n} \sin \left (2 x \right ) \]

16799

\[ {} x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \]

16800

\[ {} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \]

16801

\[ {} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \]

16802

\[ {} y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \]

16803

\[ {} 2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0 \]

16804

\[ {} y^{\prime } = \frac {1}{2 x -y^{2}} \]

16805

\[ {} x^{2}+x y^{\prime } = 3 x +y^{\prime } \]

16806

\[ {} x y y^{\prime }-y^{2} = x^{4} \]

16807

\[ {} \frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \]

16808

\[ {} \left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}} \]

16809

\[ {} x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \]

16810

\[ {} y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right ) = \cos \left (\frac {x}{2}-\frac {y}{2}\right ) \]

16811

\[ {} y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \]

16812

\[ {} x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \]

16813

\[ {} 1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \]

16814

\[ {} x^{2}+y^{2}-x y y^{\prime } = 0 \]

16815

\[ {} x -y+2+\left (x -y+3\right ) y^{\prime } = 0 \]

16816

\[ {} y+x y^{2}-x y^{\prime } = 0 \]

16817

\[ {} 2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \]

16818

\[ {} \left (x -1\right ) \left (y^{2}-y+1\right ) = \left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \]

16819

\[ {} \left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \]

16820

\[ {} \cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime } = 0 \]

16821

\[ {} y^{\prime }-1 = {\mathrm e}^{2 y+x} \]

16822

\[ {} 2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \]

16823

\[ {} x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y \]

16824

\[ {} \left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2} \]

16825

\[ {} x -y^{2}+2 x y y^{\prime } = 0 \]

16826

\[ {} x y^{\prime }+y = y^{2} \ln \left (x \right ) \]

16827

\[ {} \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0 \]

16828

\[ {} y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \]

16829

\[ {} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \]

16830

\[ {} x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0 \]

16831

\[ {} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \]

16832

\[ {} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \]

17212

\[ {} x^{\prime }+3 x = {\mathrm e}^{-2 t} \]

17213

\[ {} x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1 \]

17214

\[ {} x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right ) \]

17215

\[ {} 2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

17216

\[ {} x^{\prime }+x = 2 \sin \left (t \right ) \]

17229

\[ {} y^{\prime } = \frac {x^{4}}{y} \]

17230

\[ {} y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y} \]

17231

\[ {} y^{\prime }+y^{3} \sin \left (x \right ) = 0 \]

17232

\[ {} y^{\prime } = \frac {7 x^{2}-1}{7+5 y} \]

17233

\[ {} y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2} \]