4.19.6 Problems 501 to 600

Table 4.899: Third and higher order non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

16975

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

16976

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

16986

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

16988

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

17004

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

17006

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

17007

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

17008

\[ {} y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1 \]

17009

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

17024

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

17025

\[ {} y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \]

17026

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

17027

\[ {} y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \]

17077

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

17642

\[ {} y^{\prime \prime \prime \prime }-6 y = t \,{\mathrm e}^{-t} \]

17681

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

17682

\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right ) \]

17697

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

17709

\[ {} y^{\prime \prime \prime \prime }-16 y = g \left (t \right ) \]

17710

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = g \left (t \right ) \]

17715

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

17716

\[ {} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right ) \]

17718

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

17722

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

17724

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

17891

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

17924

\[ {} \left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = x^{4}+12 \]

17939

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

17940

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = \left (1+x \right ) {\mathrm e}^{x} \]

17951

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

18294

\[ {} y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

18295

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

18296

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

18308

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

18310

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

18311

\[ {} y^{\left (6\right )}-y = x^{10} \]

18314

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

18315

\[ {} y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1 \]

18319

\[ {} y^{\prime \prime \prime }-8 y = 16 x^{2} \]

18320

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

18321

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

18322

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

18323

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

18324

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

18325

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

18326

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

18510

\[ {} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime } = {\mathrm e}^{-3 t} \]

18511

\[ {} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

18512

\[ {} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

18514

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

18515

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

18586

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

18589

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

18590

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

18594

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

18596

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

18597

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

18598

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

18605

\[ {} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

18607

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

18608

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

18617

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

18618

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

18800

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right ) \]

18801

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

18802

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

18804

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

18805

\[ {} y^{\prime \prime \prime }+8 y = x^{4}+2 x +1 \]

18806

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

18809

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

18810

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

18817

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

18821

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

18822

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

18823

\[ {} y^{\prime \prime \prime }-13 y^{\prime }+12 y = x \]

18824

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

18825

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

18829

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

18830

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

18831

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

18833

\[ {} y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

18835

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

18836

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

18837

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

18840

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

18842

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

18843

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

18854

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

18859

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

18860

\[ {} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y = x^{2}+4 x +3 \]

18863

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

18864

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

18875

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

18876

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

18882

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

18885

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

18891

\[ {} y^{\left (5\right )}-m^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x} \]

18896

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

18906

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

18909

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