2.29 Problems 2801 to 2900

Table 2.57: Main lookup table

#

ODE

Mathematica result

Maple result

2801

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

2802

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

2803

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

2804

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

2805

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

2806

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

2807

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

2808

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

2809

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

2810

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

2811

\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]

2812

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

2813

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

2814

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

2815

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

2816

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

2817

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \]

2818

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

2819

\[ {}x y^{\prime \prime }-\left (1+2 x \right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x} \]

2820

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

2821

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \]

2822

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

2823

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

2824

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

2825

\[ {}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0 \]

2826

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

2827

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

2828

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \]

2829

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \]

2830

\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \]

2831

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

2832

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

2833

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

2834

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

2835

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

2836

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

2837

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

2838

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

2839

\[ {}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t} \]

2840

\[ {}y^{\prime }+y = 8 \,{\mathrm e}^{3 t} \]

2841

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

2842

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

2843

\[ {}y^{\prime }-y = 6 \cos \left (t \right ) \]

2844

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

2845

\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right ) \]

2846

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

2847

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

2848

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

2849

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \]

2850

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

2851

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

2852

\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \]

2853

\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \]

2854

\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \]

2855

\[ {}y^{\prime \prime }-y^{\prime }-6 y = -6 \,{\mathrm e}^{t}+12 \]

2856

\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \]

2857

\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \]

2858

\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \]

2859

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \]

2860

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

2861

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

2862

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

2863

\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \]

2864

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

2865

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]

2866

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

2867

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

2868

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

2869

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

2870

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

2871

\[ {}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

2872

\[ {}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \]

2873

\[ {}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \]

2874

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

2875

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \]

2876

\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

2877

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

2878

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]

2879

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \]

2880

\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (-3+t \right ) \]

2881

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \]

2882

\[ {}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \]

2883

\[ {}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \]

2884

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

2885

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

2886

\[ {}y^{\prime }+4 y = 3 \delta \left (t -1\right ) \]

2887

\[ {}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (-3+t \right ) \]

2888

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right ) \]

2889

\[ {}y^{\prime \prime }-4 y = \delta \left (-3+t \right ) \]

2890

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \]

2891

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

2892

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

2893

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

2894

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

2895

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]

2896

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

2897

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

2898

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

2899

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

2900

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