4.24.48 Problems 4701 to 4800

Table 4.1447: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

20273

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}} \]

20274

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

20275

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

20276

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

20277

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

20279

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

20282

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

20283

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

20285

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

20287

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

20288

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

20289

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

20290

\[ {} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

20291

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

20292

\[ {} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0 \]

20293

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

20294

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

20295

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

20296

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0 \]

20297

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

20298

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

20299

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

20300

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

20301

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

20302

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

20303

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

20304

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

20305

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

20306

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0 \]

20307

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

20308

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

20309

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

20310

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

20311

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

20312

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

20313

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

20314

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

20315

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

20316

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

20317

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

20318

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

20319

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

20320

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

20330

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

20331

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

20600

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

20601

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

20602

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

20603

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

20604

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

20605

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

20606

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

20607

\[ {} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

20608

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

20609

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

20610

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

20611

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

20612

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

20613

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \]

20614

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

20615

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

20616

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

20617

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

20618

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

20619

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

20620

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

20621

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 4 x \]

20622

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

20623

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2} \]

20624

\[ {} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = x^{2}+\frac {1}{x^{2}} \]

20625

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

20626

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

20627

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

20628

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

20629

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = \left (\ln \left (x \right )+1\right )^{2} \]

20630

\[ {} \left (2 x +5\right )^{2} y^{\prime \prime }-6 \left (2 x +5\right ) y^{\prime }+8 y = 0 \]

20631

\[ {} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right ) = \left (2 x +3\right ) \left (2 x +4\right ) \]

20632

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

20633

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

20634

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

20635

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

20636

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

20637

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

20638

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

20639

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

20640

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

20641

\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right ) \]

20642

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

20643

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

20644

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

20645

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

20646

\[ {} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+x y^{\prime }+y = \ln \left (x \right ) \]

20647

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

20648

\[ {} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

20650

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

20653

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

20654

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

20656

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

20657

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

20658

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