4.5.14 Problems 1301 to 1400

Table 4.675: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

10127

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

10128

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

10129

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

10130

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

10131

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

10132

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

10133

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

10134

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

10135

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

10136

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

10137

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

10138

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

10139

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \]

10140

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \]

10141

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

10142

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

10143

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

10147

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

10148

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

10149

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

10150

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

10151

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

10152

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

10153

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

10154

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

10155

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

10156

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

10157

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

10159

\[ {} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \]

10160

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

10161

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

10165

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

10166

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

10174

\[ {} 4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right ) \]

10239

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

10241

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

10246

\[ {} y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

10252

\[ {} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 4 \sqrt {x}\, {\mathrm e}^{x} \]

10253

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

10263

\[ {} y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x} \]

10264

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

10378

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

10379

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

10380

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

10381

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

10386

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

10387

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

10388

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

10389

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

10390

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

10391

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

10395

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

10396

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

10397

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

10398

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

10399

\[ {} y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \]

10400

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

10401

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

10402

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

10403

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

10404

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

10405

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

10406

\[ {} y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

10407

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

10408

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

10409

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

10410

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

10411

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

10412

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

10413

\[ {} y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \]

10414

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

10415

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

10437

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

10438

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = x \]

10441

\[ {} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

10442

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

10444

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

10446

\[ {} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \]

10447

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

10448

\[ {} y^{\prime \prime } \cos \left (x \right )+y^{\prime } \sin \left (x \right )-2 \cos \left (x \right )^{3} y = 2 \cos \left (x \right )^{5} \]

10449

\[ {} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \]

10450

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

10453

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \]

10454

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

10455

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

10456

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right ) \]

12298

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

12299

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

12300

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

12302

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

12303

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

12326

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

12339

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

12341

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

12351

\[ {} y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} = 0 \]

12353

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

12354

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

12372

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

12381

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

12390

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