3.27.3 Problems 201 to 300

Table 3.935: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

2740

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x} \]

2741

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

2745

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

2746

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 5 \,{\mathrm e}^{-2 x} x \]

2747

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

2748

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

2749

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

2753

\[ {}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right ) \]

2754

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

2755

\[ {}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right ) \]

2756

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

2757

\[ {}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m} \]

2758

\[ {}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x} \]

2761

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

2762

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

2763

\[ {}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right ) \]

2764

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right ) \]

2765

\[ {}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

2766

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right ) \]

2767

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2} \]

2768

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

2769

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

2770

\[ {}y^{\prime \prime }-4 y = 100 \,{\mathrm e}^{x} \sin \left (x \right ) x \]

2771

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right ) \]

2772

\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \]

2773

\[ {}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \]

2774

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right ) \]

2775

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

2776

\[ {}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3} \]

2777

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1} \]

2778

\[ {}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1} \]

2779

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right ) \]

2780

\[ {}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}} \]

2781

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4} \]

2782

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2} \]

2783

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

2784

\[ {}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1 \]

2785

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

2786

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

2787

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

2788

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

2789

\[ {}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \]

2790

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

2791

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right ) \]

2796

\[ {}y^{\prime \prime }-9 y = F \left (x \right ) \]

2797

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

2798

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

2799

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

2800

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 5 \,{\mathrm e}^{2 x} x \]

2801

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

2818

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

2821

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

2822

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

2826

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

2827

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

2831

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

2832

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

2833

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

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

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

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

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

2874

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

2875

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

2876

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

2877

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

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

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

2880

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

2881

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

2888

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

2889

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

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

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

3254

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \]

3255

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \]

3256

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