3.4.4 Problems 301 to 400

Table 3.343: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

2605

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

2619

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

2620

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

2725

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

2726

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

2727

\[ {}y^{\prime \prime }-36 y = 0 \]

2728

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

2736

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

2737

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

2810

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

2811

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]

2812

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

2813

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

2814

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

2815

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

2816

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

2817

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

2846

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

2847

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

2866

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

4572

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

4573

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

4574

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

4575

\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

4576

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

4581

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

4582

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

4584

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

4587

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

4593

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

4594

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

4596

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

4601

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

4602

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

4603

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

4604

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

4651

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

4656

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

4657

\[ {}r^{\prime \prime } = -\frac {k}{r^{2}} \]

4658

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

4659

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

4660

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

4661

\[ {}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

4662

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

4663

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

4665

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

4666

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

4667

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

4668

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

4669

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

4672

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

4673

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

4674

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

4682

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

4686

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

4732

\[ {}u^{\prime \prime }-\frac {a^{2} u}{x^{\frac {2}{3}}} = 0 \]

4733

\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

4734

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

4735

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

4736

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

4737

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

4738

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

4739

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

4740

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

4741

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

4742

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

4743

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

4744

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

4745

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

4746

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

4747

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

4791

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

4792

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

4793

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

4794

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

4795

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

4796

\[ {}y^{\prime \prime }+16 y = 0 \]

4797

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

4798

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

4799

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

4800

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

4801

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

4802

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

4839

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

4840

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

4841

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

4842

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

4843

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

4844

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

4845

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

4846

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

4848

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

4849

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

4850

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

4851

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

4858

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

4859

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

4860

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

4861

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

4862

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