What is the solution for (D^2+4)y=5e^x-4x^2 ?

The solution for (D^2+4)y=5e^x-4x^2 is y=c_{1}cos(2x)+c_{2}sin(2x)+e^x-x^2+1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(D^2+4)y=5e^x-4x^2

(D^{2} + 4) y = 5 e^{x} - 4 x^{2}

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

Solution steps

(D^{2} + 4) y = 5 e^{x} - 4 x^{2}

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y = 3 x + 5

y^{^{''}} + a y^{^{'}} + b = 0

y^{^{''}} + k y = t^{2} e^{3 t}, y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 2 y^{^{'}} + y = t^{2}, y (0) = 1, y^{^{'}} (0) = 1

What is the solution for (D^2+4)y=5e^x-4x^2 ?
The solution for (D^2+4)y=5e^x-4x^2 is y=c_{1}cos(2x)+c_{2}sin(2x)+e^x-x^2+1/2