3.1.63 Problems 6201 to 6300

Table 3.125: First order ode

#

ODE

Mathematica

Maple

13428

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

13429

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

13430

\[ {}4 x y-6+x^{2} y^{\prime } = 0 \]

13431

\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \]

13432

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

13433

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

13434

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

13435

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

13436

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

13437

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

13438

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

13439

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

13440

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

13441

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

13442

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

13443

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

13444

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

13445

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

13446

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

13447

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

13448

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

13449

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

13450

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

13451

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

13452

\[ {}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \]

13453

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

13454

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

13455

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

13456

\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \]

13457

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

13458

\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \]

13459

\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \]

13460

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

13461

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

13462

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

13463

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

13464

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

13465

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

13466

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

13467

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

13468

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

13469

\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \]

13470

\[ {}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \]

13471

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

13472

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

13530

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

13849

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

13850

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

13851

\[ {}y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \]

13884

\[ {}y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]

13885

\[ {}y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]

13889

\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

13892

\[ {}y^{\prime } = 3 \delta \left (t -2\right ) \]

13893

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

13896

\[ {}y^{\prime }+2 y = 4 \delta \left (-1+t \right ) \]

13899

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

14046

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

14048

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

14052

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

14053

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

14054

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

14055

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

14056

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

14066

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

14067

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

14068

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

14069

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

14070

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

14071

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

14072

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

14073

\[ {}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

14074

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

14075

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

14076

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

14077

\[ {}y^{\prime } = \frac {-2 x -10}{\left (2+x \right ) \left (x -4\right )} \]

14078

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

14079

\[ {}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \]

14080

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

14081

\[ {}y^{\prime } = \frac {1}{x^{2}-16} \]

14082

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

14083

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

14084

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

14085

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

14092

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

14093

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

14094

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

14095

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

14096

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

14097

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

14098

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

14101

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

14102

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

14106

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

14107

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

14114

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

14115

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

14116

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

14117

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

14118

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

14119

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