4.12.13 Problems 1201 to 1300

Table 4.839: Third and higher order linear ODE

#

ODE

Mathematica

Maple

Sympy

18305

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

18306

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

18307

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

18308

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

18316

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

18318

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

18319

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

18322

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

18323

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

18327

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

18328

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

18329

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

18330

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

18331

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

18332

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

18333

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

18334

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

18513

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

18518

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

18519

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

18520

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

18521

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

18522

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

18523

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

18527

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

18534

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

18546

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

18586

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

18587

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

18588

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

18589

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

18590

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

18591

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

18592

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

18594

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

18597

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

18598

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

18602

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

18604

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

18605

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

18606

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

18613

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

18615

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

18616

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

18617

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

18625

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

18626

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

18800

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

18801

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

18803

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

18804

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

18808

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

18809

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

18810

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

18812

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

18813

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

18814

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

18817

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

18818

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

18823

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

18824

\[ {} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0 \]

18825

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

18829

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

18830

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

18831

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

18832

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

18833

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

18837

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

18838

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

18839

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

18841

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

18843

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

18844

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

18845

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

18848

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

18850

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

18851

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

18854

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

18855

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

18862

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

18864

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

18866

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

18867

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

18868

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

18871

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

18872

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

18876

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

18883

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

18884

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

18890

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

18898

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

18899

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

18900

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

18913

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

18914

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

18915

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

18917

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

18921

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

18924

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

18926

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