5.9.53 Problems 5201 to 5300

Table 5.733: First order ode linear in derivative

#

ODE

Mathematica

Maple

13382

\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \]

13383

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

13384

\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \]

13385

\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \]

13386

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

13387

\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \]

13388

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

13644

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

13645

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

13704

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

13705

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

13706

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

13707

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

13708

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

13709

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

13710

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

13711

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

13712

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

13713

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

13714

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

13715

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

13716

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

13717

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

13718

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

13719

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

13720

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

13721

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

13722

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

13723

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

13724

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

13725

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

13726

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

13727

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

13728

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

13729

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

13730

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

13731

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

13732

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

13733

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

13734

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

13735

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

13736

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

13737

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

13738

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

13739

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

13740

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

13741

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

13742

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

13743

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

13744

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

13745

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

13746

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

13747

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

13748

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

13749

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

13848

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

13849

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

13850

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

13851

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

13852

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

13853

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

13854

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

13855

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

13856

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

13857

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

13860

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

13862

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

13864

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

13867

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

13868

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

13869

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

13870

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

13871

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

13872

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

13875

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

13876

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

13877

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

13878

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

13879

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

13882

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

13883

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

13885

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

13887

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

13888

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

13889

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

13890

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

13891

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

13892

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

13893

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

13894

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

13895

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

13896

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

13948

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

13949

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

13950

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

13951

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

13952

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

13953

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

13954

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

13955

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