4.12.10 Problems 901 to 1000

Table 4.1097: Third and higher order linear ODE

#

ODE

Mathematica

Maple

Sympy

14207

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \]

14208

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

14209

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

14210

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

14212

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

14215

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

14217

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

14224

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

14225

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

14226

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

14228

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

14229

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

14230

\[ {} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 10 x +\frac {10}{x} \]

14234

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

14236

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

14237

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

14238

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

14239

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

14242

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

14244

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

14245

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

14278

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

14279

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

14280

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

14283

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

14287

\[ {} x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

14296

\[ {} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0 \]

14303

\[ {} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0 \]

14458

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

14459

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

14460

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

14461

\[ {} x^{\prime \prime \prime }-x^{\prime }-8 x = 0 \]

14462

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

14463

\[ {} x^{\prime \prime \prime }-8 x = 0 \]

14464

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

14536

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

14537

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

14538

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

14549

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

14678

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14679

\[ {} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \]

14692

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

14693

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

14700

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \]

14701

\[ {} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \]

14702

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

14703

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

14704

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

14705

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \]

14706

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

14707

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

14708

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y = 0 \]

14709

\[ {} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y = 0 \]

14710

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

14711

\[ {} y^{\left (5\right )} = 0 \]

14726

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

14727

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \]

14728

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

14729

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y = 0 \]

14730

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

14731

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y = 0 \]

14740

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \]

14741

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \]

14742

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \]

14743

\[ {} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \]

14746

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \]

14747

\[ {} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \]

14748

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

14749

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

14750

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \]

14751

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \]

14754

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \]

14755

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \]

14770

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

14771

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \]

14777

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

14778

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

14779

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

14780

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

14781

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

14782

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

14783

\[ {} y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \]

14784

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

14785

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (2 x \right ) \sin \left (x \right ) \]

14811

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

14822

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

14823

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

14824

\[ {} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0 \]

14830

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

14935

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right ) \]

14936

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t} \]

14944

\[ {} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0 \]

14946

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

15061

\[ {} x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

15062

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

15063

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

15064

\[ {} x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \]

15183

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

15191

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

15193

\[ {} x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]