What is the solution for (d^2-4d+4)*y=8e^{2x}*x^2*sin^2(x) ?

The solution for (d^2-4d+4)*y=8e^{2x}*x^2*sin^2(x) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2-4d+4)y=8e^{2x}x^2*sin^2(x)

(d^{2} - 4 d + 4) \cdot y = 8 e^{2 x} \cdot x^{2} \cdot sin^{2} (x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

Solution steps

(d^{2} - 4 d + 4) y = 8 e^{2 x} x^{2} sin^{2} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t - 8

(d^{3} - 2 d + 4) y = 3 x^{2} - 5 x + 2

(d^{3} - 3 d^{2} + 4 d - 2) \cdot y = e^{x} + cos (x) + x

(d^{4} + d^{2} + 16) y = 16 x^{2} + 256

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{- 5} x

What is the solution for (d^2-4d+4)*y=8e^{2x}*x^2*sin^2(x) ?
The solution for (d^2-4d+4)*y=8e^{2x}*x^2*sin^2(x) is