4.24.8 Problems 701 to 800

Table 4.1025: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

8494

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

8495

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

8496

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

8497

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

8498

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

8499

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

8501

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

8502

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

8503

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

8504

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

8505

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

8506

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

8507

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

8508

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

8509

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

8510

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

8511

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

8512

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

8513

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

8514

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

8515

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

8516

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

8517

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

8518

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

8519

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

8520

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

8521

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

8522

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

8523

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

8524

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

8525

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

8526

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

8527

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

8528

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

8572

\[ {} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

8606

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

8607

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

8608

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

8609

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \]

8610

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

8611

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

8612

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

8613

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

8614

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0 \]

8615

\[ {} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

8626

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

8657

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

8759

\[ {} t y^{\prime \prime }+4 y^{\prime } = t^{2} \]

8760

\[ {} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \]

8761

\[ {} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \]

8762

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

8763

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

8764

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

8765

\[ {} t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0 \]

8774

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

8775

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

8776

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

8778

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

8779

\[ {} 3 y y^{\prime \prime }+y = 5 \]

8780

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

8781

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

8799

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

8803

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

8805

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

8806

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

8807

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

8808

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

8809

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

8810

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

8811

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

8812

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

8813

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

8814

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

8815

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

8816

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

8817

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

8818

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

8819

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

8820

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

8821

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

8822

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

8823

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

8824

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

8825

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

8826

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

8827

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

8828

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

8829

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

8830

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

8831

\[ {} y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0 \]

8832

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

8833

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

8834

\[ {} y^{\prime \prime }-x y-x^{6}+64 = 0 \]

8835

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

8836

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

8837

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

8838

\[ {} y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

8839

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

8840

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

8841

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