4.5.31 Problems 3001 to 3100

Table 4.709: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

21832

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

21833

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \]

21834

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \]

21835

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \]

21836

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

21873

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

21874

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

21877

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

21881

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

21905

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

21909

\[ {} y^{\prime \prime }+y^{\prime } = 6 y+5 \,{\mathrm e}^{2 x} \]

21999

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

22000

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

22001

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

22002

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

22003

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

22005

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

22007

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

22030

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

22031

\[ {} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right ) \]

22032

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

22036

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

22037

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

22039

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

22049

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

22050

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

22052

\[ {} x y^{\prime \prime }+y^{\prime } = 16 x^{3} \]

22061

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

22063

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

22066

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

22067

\[ {} s^{2} t^{\prime \prime }+s t t^{\prime } = s \]

22069

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

22072

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

22075

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

22079

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

22087

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

22204

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

22245

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

22246

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

22247

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

22249

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

22254

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

22255

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

22256

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

22257

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

22258

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

22264

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

22265

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

22268

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \]

22269

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

22270

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

22271

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

22272

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

22274

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

22275

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

22276

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (x \right ) \]

22278

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

22279

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

22281

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

22282

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

22283

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

22285

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

22349

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

22350

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right ) \]

22351

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

22352

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

22353

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \]

22361

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

22362

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

22363

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

22364

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

22365

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

22366

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 t} \]

22367

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (t -4\right ) \]

22397

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 9 x \]

22399

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

22404

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

22405

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

22407

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

22410

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

22414

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 6 \,{\mathrm e}^{x} \]

22418

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

22422

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

22424

\[ {} y^{\prime \prime } = 12 x \left (4-x \right ) \]

22426

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

22427

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

22441

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

22443

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

22447

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

22472

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

22575

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

22593

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

22597

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

22598

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

22600

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

22605

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

22607

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

22613

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

22658

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

22690

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