4.9.53 Problems 5201 to 5300

Table 4.729: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

13565

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

13566

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

13625

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

13626

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

13627

\[ {} u^{\prime } = 4 t \ln \left (t \right ) \]

13628

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

13629

\[ {} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

13630

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

13631

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

13632

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

13633

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

13634

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

13635

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

13636

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

13637

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

13638

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

13639

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

13640

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

13641

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

13642

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

13643

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

13644

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

13645

\[ {} x^{\prime }+p x = q \]

13646

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

13647

\[ {} i^{\prime } = p \left (t \right ) i \]

13648

\[ {} x^{\prime } = \lambda x \]

13649

\[ {} m v^{\prime } = -m g +k v^{2} \]

13650

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

13651

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

13652

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

13653

\[ {} x^{\prime }+t x = 4 t \]

13654

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

13655

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

13656

\[ {} x^{\prime }+x \tanh \left (t \right ) = 3 \]

13657

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

13658

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

13659

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

13660

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

13661

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

13662

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

13663

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

13664

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

13665

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

13666

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

13667

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

13668

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

13669

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

13670

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

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

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

13781

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

13783

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

13785

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

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

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

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

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

13803

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

13804

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

13806

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

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

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

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

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

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

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

13889

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

13974

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

13978

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