4.1.65 Problems 6401 to 6500

Table 4.129: First order ode

#

ODE

Mathematica

Maple

Sympy

15491

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

15492

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

15493

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

15494

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

15495

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

15496

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

15497

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

15498

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

15499

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

15500

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

15501

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

15502

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

15503

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

15504

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

15505

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

15506

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

15507

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

15508

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

15509

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

15510

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

15511

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

15563

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

15564

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

15566

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

15567

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

15569

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

15570

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

15571

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

15575

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

15576

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

15598

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

15602

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

15603

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

15604

\[ {} y^{\prime }-2 \sqrt {{| y|}} = 0 \]

15605

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

15606

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

15608

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

15609

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

15613

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

15617

\[ {} {y^{\prime }}^{2}-4 y = 0 \]

15618

\[ {} {y^{\prime }}^{2}-9 x y = 0 \]

15619

\[ {} {y^{\prime }}^{2} = x^{6} \]

15620

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

15621

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

15623

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

15625

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

15626

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

15638

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

15639

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

15640

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

15641

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

15642

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

15643

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

15644

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

15645

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

15646

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

15647

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

15648

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

15649

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

15650

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

15651

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

15652

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

15653

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

15654

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

15655

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

15656

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

15657

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

15658

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

15659

\[ {} y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \]

15660

\[ {} y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \]

15661

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

15662

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

15663

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

15664

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

15665

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

15666

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

15667

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

15668

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

15669

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

15670

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

15671

\[ {} y^{\prime } = -\frac {y}{x}+y^{{1}/{4}} \]

15672

\[ {} y^{\prime } = 4 y-5 \]

15673

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

15674

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

15675

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

15676

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

15677

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

15678

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

15679

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

15680

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

15681

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

15682

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

15683

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

15684

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

15685

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

15686

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

15687

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

15688

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

15689

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

15690

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