4.1.62 Problems 6101 to 6200

Table 4.123: First order ode

#

ODE

Mathematica

Maple

Sympy

13769

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

13770

\[ {} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

13771

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

13772

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

13773

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

13774

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

13775

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

13776

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

13777

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

13778

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

13779

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

13780

\[ {} {y^{\prime }}^{2} = 9 y^{4} \]

13781

\[ {} x^{\prime } = {\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \]

13782

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

13783

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

13784

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

13785

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

13786

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

13787

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

13788

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

13789

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

13790

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

13791

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

13792

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

13793

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

13794

\[ {} {y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime } = 0 \]

13795

\[ {} y = 5 x y^{\prime }-{y^{\prime }}^{2} \]

13796

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

13797

\[ {} y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2 \]

13798

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

13799

\[ {} x^{\prime }+5 x = 10 t +2 \]

13800

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

13801

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

13802

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

13803

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

13804

\[ {} x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

13805

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

13806

\[ {} y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0 \]

13807

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

13808

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

13809

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

13810

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

13811

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

13812

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

13813

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

13814

\[ {} \left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0 \]

13815

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

13816

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

13817

\[ {} 3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \]

13818

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

13819

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

13820

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

13869

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

13870

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

13871

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

13872

\[ {} x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime } \]

13873

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

13874

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

13875

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

13876

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

13877

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

13878

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

13885

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

13887

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

13888

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

13889

\[ {} 5 y^{\prime }-x y = 0 \]

13890

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

13896

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

13974

\[ {} 2 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \]

13978

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

13980

\[ {} y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -2\right ) \]

13981

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

14001

\[ {} 10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

14075

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

14076

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

14077

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

14078

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

14083

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

14084

\[ {} \left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0 \]

14085

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

14086

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

14087

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

14088

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

14089

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

14090

\[ {} 1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \]

14091

\[ {} r^{\prime }+r \tan \left (t \right ) = 0 \]

14092

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

14093

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

14094

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

14095

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

14096

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

14097

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

14098

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

14099

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

14100

\[ {} 8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0 \]

14101

\[ {} 2 \sqrt {s t}-s+t s^{\prime } = 0 \]

14102

\[ {} t -s+t s^{\prime } = 0 \]

14103

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

14104

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

14105

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