3.1.28 Problems 2701 to 2800

Table 3.55: First order ode

#

ODE

Mathematica

Maple

4683

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

4684

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

4685

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

4687

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

4688

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

4689

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

4690

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

4691

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

4692

\[ {}y^{\prime }+b^{2} y^{2} = a^{2} \]

4693

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

4694

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

4695

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

4731

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

4748

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

4749

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

4750

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

4751

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

4752

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

4753

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

4754

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

4755

\[ {}y y^{\prime }+x y^{2}-8 x = 0 \]

4756

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

4757

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

4758

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

4759

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

4760

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

4761

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

4762

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

4763

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

4764

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

4765

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

4766

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

4767

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

4768

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

4769

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

4770

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

4771

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

4772

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

4773

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

4774

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

4775

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

4776

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

4777

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

4778

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

4779

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

4780

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

4781

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

4782

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

4783

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

4784

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

4785

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

4786

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

4787

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

4788

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

4789

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

4790

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

4864

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

4865

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

4868

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

4870

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

4872

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

4873

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

4874

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

4880

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

4881

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

4882

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

4884

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

4886

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

4888

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

4889

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

4893

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

4895

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

4897

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

4912

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

4913

\[ {}y^{\prime } = 4 y^{2}-3 y+1 \]

4914

\[ {}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

4915

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

4916

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

4917

\[ {}s^{2}+s^{\prime } = \frac {s+1}{s t} \]

4918

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

4919

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

4920

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

4921

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

4922

\[ {}x v^{\prime } = \frac {1-4 v^{2}}{3 v} \]

4923

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

4924

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

4925

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

4926

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

4927

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

4928

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

4929

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

4930

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

4931

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

4932

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

4933

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

4934

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

4935

\[ {}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \]

4936

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

4937

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

4938

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