4.3.88 Problems 8701 to 8800

Table 4.539: Second order ode

#

ODE

Mathematica

Maple

Sympy

24998

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

24999

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

25000

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

25001

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

25002

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

25003

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

25004

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

25005

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

25006

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

25007

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

25008

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

25009

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

25010

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

25011

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

25012

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

25013

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

25014

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

25015

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

25016

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

25017

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

25018

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

25019

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

25020

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

25021

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

25022

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

25023

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

25024

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

25027

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

25043

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

25044

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25051

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25181

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

25182

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

25183

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

25184

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

25185

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 0 \]

25186

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 t} \]

25187

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

25188

\[ {} y^{\prime \prime }+4 y = 8 \]

25189

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 9 \,{\mathrm e}^{2 t} \]

25190

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{2 t} \]

25191

\[ {} y^{\prime \prime }-4 y^{\prime }-5 y = 150 t \]

25192

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 4 \cos \left (2 t \right ) \]

25193

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

25194

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \]

25195

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 4 \cos \left (2 t \right ) \]

25196

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 50 \sin \left (t \right ) \]

25197

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

25198

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

25199

\[ {} y^{\prime \prime }+y = 4 \sin \left (t \right ) \]

25200

\[ {} y^{\prime \prime }+9 y = 36 t \sin \left (3 t \right ) \]

25201

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

25202

\[ {} y^{\prime \prime }+4 y = 32 t \cos \left (2 t \right ) \]

25203

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

25204

\[ {} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{t} \]

25206

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

25208

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = {\mathrm e}^{-t} \]

25209

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

25210

\[ {} y^{\prime \prime }+8 y = t \]

25211

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

25212

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25213

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

25214

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

25215

\[ {} y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

25216

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

25217

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 0 \]

25218

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25219

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

25220

\[ {} 2 y^{\prime \prime }-12 y^{\prime }+18 y = 0 \]

25221

\[ {} y^{\prime \prime }+13 y^{\prime }+36 y = 0 \]

25222

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

25223

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = 0 \]

25224

\[ {} y^{\prime \prime }-4 y^{\prime }-21 y = 0 \]

25225

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

25226

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

25227

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

25228

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

25229

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{2 t} \]

25230

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{2 t} \]

25231

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

25232

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

25233

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

25234

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-3 t} \]

25235

\[ {} y^{\prime \prime }+4 y = 1+{\mathrm e}^{t} \]

25236

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

25237

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{t} \]

25238

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

25239

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

25240

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{2 t} \]

25241

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 25 t \,{\mathrm e}^{-3 t} \]

25242

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \]

25243

\[ {} y^{\prime \prime }-8 y^{\prime }+25 y = 104 \sin \left (3 t \right ) \]

25244

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 t} \]

25245

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \,{\mathrm e}^{-t} \]

25246

\[ {} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 t} \]

25247

\[ {} y^{\prime \prime }-4 y = 2-8 t \]

25248

\[ {} y^{\prime \prime }-4 y = {\mathrm e}^{-6 t} \]

25249

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 16 \,{\mathrm e}^{t} \]

25250

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 t} \]

25251

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