en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{''}+4x=e

Solution

x^{^{''}} + 4 x = e

Solution

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{e}{4}

Solution steps

x^{''} (t) + 4 x = e

Solve linear ODE:

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{e}{4}

x = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{e}{4}

Graph

Popular Examples

y^{''}+y^'-2y=-sin(2x)

y^{^{''}} + y^{^{'}} - 2 y = - sin (2 x)

(d^2y)/(dx^2)=(dy)/(dx)+x

\frac{d ^{2} y}{d x ^{2}} = \frac{d y}{d x} + x

y^{''}+9y=6*sin(3x)-6*cos(-3x)+36*e^{3x}

y^{^{''}} + 9 y = 6 \cdot sin (3 x) - 6 \cdot cos (- 3 x) + 36 \cdot e^{3 x}

y^{''}-49y=2xe^{7x}

y^{^{''}} - 49 y = 2 x e^{7 x}

(D^2+4)y=xsin(x)

(D^{2} + 4) y = x sin (x)

Frequently Asked Questions (FAQ)

What is the solution for x^{''}+4x=e ?
The solution for x^{''}+4x=e is x=c_{1}cos(2t)+c_{2}sin(2t)+e/4