3.9.23 Problems 2201 to 2300

Table 3.551: First order ode linear in derivative

#

ODE

Mathematica

Maple

4528

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

4529

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

4530

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

4531

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

4532

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

4533

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

4534

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

4535

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

4536

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

4537

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

4538

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

4539

\[ {}y^{\prime }+8 y^{3} x^{3}+2 x y = 0 \]

4540

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

4541

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

4542

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

4543

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

4544

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

4545

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

4546

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

4547

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

4548

\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \]

4549

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

4550

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

4551

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

4552

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

4553

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

4554

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

4555

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

4556

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

4557

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

4558

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

4559

\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

4560

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

4561

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

4562

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

4563

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

4564

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

4565

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

4566

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

4567

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

4568

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

4569

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

4570

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

4571

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

4675

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

4676

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

4677

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-1-a} = 0 \]

4678

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

4679

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

4680

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

4681

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

4685

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

4687

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

4688

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

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

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

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

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