4.9.74 Problems 7301 to 7400

Table 4.985: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

20411

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

20413

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

20414

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

20415

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

20416

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

20417

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

20418

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

20419

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

20420

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

20421

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

20422

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

20423

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

20424

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

20426

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

20427

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

20428

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

20429

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

20430

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

20431

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

20432

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

20433

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

20434

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

20435

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

20436

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

20437

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

20438

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

20439

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

20440

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

20441

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

20442

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

20443

\[ {} y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

20522

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

20550

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

20562

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

20564

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

20565

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

20567

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

20597

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

20598

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

20793

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

20794

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

20795

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

20796

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

20797

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

20798

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

20799

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

20800

\[ {} y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6} \]

20801

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

20802

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

20803

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

20804

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

20805

\[ {} y^{\prime }+p \left (x \right ) y = q \left (x \right ) y^{n} \]

20806

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

20807

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

20808

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

20809

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

20810

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

20811

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

20812

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

20844

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

20927

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

20928

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

20929

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

20930

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

20931

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

20932

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

20933

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

20934

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

20935

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

20936

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

20937

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

20938

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

20939

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

20940

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

20941

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

20942

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

20945

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

20946

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

20947

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

20948

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

20949

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

20950

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

20951

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

20952

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

21064

\[ {} y^{\prime } = k y-c y^{2} \]

21065

\[ {} y^{\prime } = y^{2}-6 y-16 \]

21066

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

21067

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

21068

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

21069

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

21070

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

21071

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

21072

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

21073

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

21074

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

21075

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

21076

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

21077

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

21078

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

21079

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