4.1.77 Problems 7601 to 7700

Table 4.153: First order ode

#

ODE

Mathematica

Maple

Sympy

17372

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

17373

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

17374

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

17375

\[ {} 4 x y y^{\prime } = 8 x^{2}+5 y^{2} \]

17376

\[ {} y^{\prime }+y-y^{{1}/{4}} = 0 \]

17464

\[ {} x^{\prime } = \frac {x \sqrt {6 x-9}}{3} \]

17812

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

17813

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

17815

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

17816

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

17817

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

17818

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

17819

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

17820

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

17821

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

17822

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

17823

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

17824

\[ {} \left (x +2 y+1\right ) y^{\prime } = 2 x +4 y+3 \]

17825

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

17826

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

17827

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

17828

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

17829

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

17830

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

17831

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

17832

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

17833

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

17834

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

17835

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

17836

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

17837

\[ {} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0 \]

17838

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

17839

\[ {} y^{\prime } = y^{2}+\frac {1}{x^{4}} \]

17840

\[ {} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}} \]

17841

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

17842

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

17843

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

17844

\[ {} y^{\prime } = k y+f \left (x \right ) \]

17845

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

17846

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

17847

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

17848

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

17849

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

17850

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

17851

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

17852

\[ {} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0 \]

17853

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

17854

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

17855

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

17856

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

17857

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

17858

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

17859

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

17860

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

17861

\[ {} x {y^{\prime }}^{3} = 1+y^{\prime } \]

17862

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

17863

\[ {} {y^{\prime }}^{3}+y^{3}-3 y y^{\prime } = 0 \]

17864

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

17865

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

17866

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

17867

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

17868

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

17869

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

17870

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

17871

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

17872

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

17873

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

17874

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

17875

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

17876

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

17877

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

17878

\[ {} y^{\prime } = \sqrt {y} \]

17879

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

17880

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

17881

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

17882

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

17883

\[ {} {y^{\prime }}^{2} x -2 y y^{\prime }+4 x = 0 \]

17884

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

17885

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

17886

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

17887

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

17888

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

17889

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

17890

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

17977

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

17978

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

17979

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

17980

\[ {} y^{\prime } = k y \]

17983

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

17984

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

17985

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

17986

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

17987

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

17988

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

17989

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

17990

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

17991

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

17992

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

17993

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

17994

\[ {} y^{\prime } = \arcsin \left (x \right ) \]