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Popular >

x^{''}+4x=1

Solution

x^{^{''}} + 4 x = 1

Solution

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

Solution steps

x^{''} (t) + 4 x = 1

Solve linear ODE:

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

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

Popular Examples

y^{''}+y=5xsin(5x)

y^{^{''}} + y = 5 x sin (5 x)

(D^4+2D^3+2D^2)y=2xe^{-x}

(D^{4} + 2 D^{3} + 2 D^{2}) y = 2 x e^{- x}

(d^2y)/(dx^2)+4(dy)/(dx)-12=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 = 0

y^{''}+4y^'+5y=(2e^{2x})/(sin(x))

y^{^{''}} + 4 y^{^{'}} + 5 y = \frac{2 e ^{2 x}}{sin ( x )}

y^{''}+9y=t^2e^{3t}

y^{^{''}} + 9 y = t^{2} e^{3 t}

Frequently Asked Questions (FAQ)

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