4.29.5 Problems 401 to 500

Table 4.1619: Second order, Linear, non-homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

15265

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

15268

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

15269

\[ {} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]

15270

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

15276

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

15277

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

15280

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

15283

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

15284

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

15285

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

15296

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

15298

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

15299

\[ {} y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

15368

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

15369

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

15370

\[ {} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t \]

15371

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

15372

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

15415

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

15434

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

15439

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

15517

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

15519

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

15769

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

15770

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

15771

\[ {} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

15772

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

15782

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

16272

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

16294

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

16496

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

16524

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

16530

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

16536

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

16549

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

16575

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

16576

\[ {} x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

16577

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

16578

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

16706

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \]

16712

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \]

16713

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

16714

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \]

16715

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \]

16716

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \]

16717

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \]

16718

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \]

16792

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

16793

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

16794

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

16795

\[ {} x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

16796

\[ {} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \]

16797

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

16798

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

16799

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right ) \]

16800

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

16806

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

16807

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

16808

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

16809

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

16810

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

16811

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

16812

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

16813

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

16814

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]

16828

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

16856

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

16859

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

16861

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \]

16864

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

16865

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

16870

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

16871

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

17288

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

17641

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

17642

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

17643

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \]

17647

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

17649

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

17651

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]

17652

\[ {} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \]

17653

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

17747

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

17748

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3} \]

17749

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

17750

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

17751

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

17752

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \]

17753

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

17754

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2} \]

17765

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

17766

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

17767

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

17768

\[ {} 9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \]

17777

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

17779

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

17784

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

17900

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

18196

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

18204

\[ {} y^{\prime \prime } \left (x +2\right )^{5} = 1 \]