4.7.20 Problems 1901 to 2000

Table 4.787: Solved using series method

#

ODE

Mathematica

Maple

Sympy

21786

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

21787

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

21788

\[ {} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y = 0 \]

21789

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

21790

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

21791

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

21792

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

21793

\[ {} 18 x^{2} y^{\prime \prime }+3 x \left (x +5\right ) y^{\prime }-\left (10 x +1\right ) y = 0 \]

21794

\[ {} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0 \]

21795

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

21796

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

21797

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

21798

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

21799

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

21800

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

21801

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

21802

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

21803

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

21804

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

21805

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

21806

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

21807

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

21808

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

21809

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

21810

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

21811

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

21812

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

21813

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

21814

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

21815

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

21816

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

21817

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

21818

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

21847

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

22016

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

22017

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

22018

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

22019

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

22020

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

22021

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

22022

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

22023

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

22024

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

22058

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

22059

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

22286

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

22287

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

22288

\[ {} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0 \]

22289

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

22290

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

22291

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

22292

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

22293

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

22294

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

22295

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

22296

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

22297

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

22298

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

22299

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

22300

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

22301

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

22302

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

22303

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

22304

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

22305

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

22306

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

22307

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

22308

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

22309

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

22310

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

22311

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

22312

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

22313

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

22314

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

22315

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

22316

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

22317

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

22318

\[ {} 8 x^{2} y^{\prime \prime }+10 x y^{\prime }+\left (x -1\right ) y = 0 \]

22319

\[ {} 2 x^{2} y^{\prime \prime }+7 x \left (1+x \right ) y^{\prime }-3 y = 0 \]

22320

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

22321

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

22322

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

22323

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

22324

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

22325

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

22326

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

22327

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

22328

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

22329

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

22330

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

22331

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

22332

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

22333

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

22334

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

22335

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

22336

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

22337

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

22338

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

22339

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

22340

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