4.3.80 Problems 7901 to 8000

Table 4.523: Second order ode

#

ODE

Mathematica

Maple

Sympy

22801

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

22802

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

22803

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

22804

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

22805

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x}+15 x \]

22806

\[ {} 4 i^{\prime \prime }+i = t^{2}+2 \cos \left (4 t \right ) \]

22808

\[ {} y^{\prime \prime }+16 y = 5 \sin \left (x \right ) \]

22809

\[ {} s^{\prime \prime }-3 s^{\prime }+2 s = 8 t^{2}+12 \,{\mathrm e}^{-t} \]

22810

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

22811

\[ {} L q^{\prime \prime }+R q^{\prime }+\frac {q}{c} = E_{0} \sin \left (\omega t \right ) \]

22812

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

22813

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \]

22814

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

22815

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

22816

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

22817

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

22818

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

22820

\[ {} i^{\prime \prime }+9 i = 12 \cos \left (3 t \right ) \]

22821

\[ {} s^{\prime \prime }+s^{\prime } = t +{\mathrm e}^{-t} \]

22823

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

22824

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

22825

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

22826

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

22827

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

22829

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

22830

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

22831

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

22832

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

22833

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

22834

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

22835

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

22837

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

22838

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

22839

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

22841

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

22842

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

22843

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

22844

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

22845

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

22846

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

22847

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

22848

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

22849

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

22850

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

22851

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

22854

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

22855

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

22856

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

22857

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

22858

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

22859

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

22860

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

22861

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

22863

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

22865

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

22866

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

22867

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

22868

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

22869

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

22870

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

22871

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

22872

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = x^{2}+16 \ln \left (x \right )^{2} \]

22873

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

22874

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

22875

\[ {} y^{\prime \prime } = \frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \]

22876

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

22877

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

22881

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

22882

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

22883

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

22884

\[ {} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y = 24 x^{2} \]

22885

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

22886

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

22887

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

22888

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

22889

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

22890

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

22891

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

22892

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

22893

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

22894

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

22896

\[ {} i^{\prime \prime }+2 i^{\prime }+5 i = 34 \cos \left (2 t \right ) \]

22898

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

22899

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

22902

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

22903

\[ {} r^{\prime \prime }-2 r = -{\mathrm e}^{-2 t} \]

22905

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

22906

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

22908

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

22913

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

22914

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

22917

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

22918

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

22919

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

22921

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

22922

\[ {} Q^{\prime \prime }+k Q = e \left (t \right ) \]

22923

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

22924

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

22925

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

22926

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