4.2.70 Problems 6901 to 7000

Table 4.345: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

22927

\[ {} y^{\prime \prime }+9 y = 20 \,{\mathrm e}^{-t} \]

22928

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

22929

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 100 \]

22932

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

22933

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

22935

\[ {} y^{\prime \prime }+y = 3 \delta \left (t -\pi \right ) \]

22936

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

23115

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

23116

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

23117

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

23118

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

23119

\[ {} 3 x^{\prime \prime }+19 x^{\prime }-14 x = 0 \]

23120

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

23121

\[ {} y^{\prime \prime }-9 y^{\prime }+18 y = 0 \]

23122

\[ {} y^{\prime \prime }-2 y^{\prime }-63 y = 0 \]

23123

\[ {} 20 y^{\prime \prime }-3 y^{\prime }-2 y = 0 \]

23124

\[ {} 35 y^{\prime \prime }-29 y^{\prime }+6 y = 0 \]

23125

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

23126

\[ {} 12 x^{\prime \prime }-25 x^{\prime }+12 x = 0 \]

23127

\[ {} 38 x^{\prime \prime }+10 x^{\prime }-3 x = 0 \]

23128

\[ {} 2 y^{\prime \prime }-15 y^{\prime }+27 y = 0 \]

23129

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

23130

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

23131

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

23132

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

23133

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

23134

\[ {} x^{\prime \prime }+36 x = 0 \]

23135

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

23136

\[ {} z^{\prime \prime }+g z = 0 \]

23137

\[ {} 9 y^{\prime \prime }+49 y = 0 \]

23138

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

23139

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

23140

\[ {} z^{\prime \prime }-7 z^{\prime }-13 z = 0 \]

23141

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

23142

\[ {} y^{\prime \prime }-5 y^{\prime }+8 y = 0 \]

23143

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

23144

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

23145

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

23146

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

23147

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

23148

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

23149

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