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Popular >

x^{''}+4x=4t

Solution

x^{^{''}} + 4 x = 4 t

Solution

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

Solution steps

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

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}+16y=g(t),y(0)=3,y^'(0)=0

y^{^{''}} + 16 y = g (t), y (0) = 3, y^{^{'}} (0) = 0

(d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2+8x+9

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = x^{2} + 8 x + 9

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

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

y^{''}-2y^'+y=x+e^x

y^{^{''}} - 2 y^{^{'}} + y = x + e^{x}

y^{''}+4y^'=tan(2x)

y^{^{''}} + 4 y^{^{'}} = tan (2 x)

Frequently Asked Questions (FAQ)

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