5.4.5 Problems 401 to 500

Table 5.423: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

3100

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

3221

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

3222

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \]

3223

\[ {}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \]

3224

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0 \]

3245

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

3246

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

3248

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

3250

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

3251

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

3252

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

3258

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

3259

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

3260

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

3262

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

3263

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

3264

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

3266

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

3267

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

3268

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

3270

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

3271

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

3273

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

3274

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

3275

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

3276

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

3278

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

3279

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

3280

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

3281

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

3282

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

3283

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

3284

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

3483

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

3485

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

3495

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

3558

\[ {}y^{\prime \prime }-25 y = 0 \]

3559

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

3560

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

3563

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

3564

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

3565

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

3566

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

3567

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

3570

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

3571

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

3572

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

3573

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

3574

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

3575

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

3576

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

3590

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

3591

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

3696

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

3697

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

3698

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

3699

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

3707

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

3708

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

3781

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

3782

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

3783

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

3784

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

3785

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

3786

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

3787

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

3788

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

3935

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

3936

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

3955

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

4118

\[ {}y^{\prime \prime }+8 y^{\prime }+15 y = 0 \]

4119

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

4120

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

4121

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

4122

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

4123

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

4124

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

4125

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

4126

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

4127

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

4128

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

4139

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

4161

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

4163

\[ {}25 y^{\prime \prime }-30 y^{\prime }+9 y = 0 \]

4407

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

4432

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

4436

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

5916

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

5917

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

5918

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

5919

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

5920

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

5925

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

5926

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

5928

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

5931

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

5937

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

5938

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

5940

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

5945

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