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Popular >

x^{''}+x=2e^t

Solution

x^{^{''}} + x = 2 e^{t}

Solution

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

Solution steps

x^{''} (t) + x = 2 e^{t}

Solve linear ODE:

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

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

Graph

Popular Examples

y^{'''}-3y^{''}+4y=12e^{2x}+4e^{3x}

y^{^{'''}} - 3 y^{^{''}} + 4 y = 12 e^{2 x} + 4 e^{3 x}

y^{''}-4y^'+4y=2x^2+4xe^{2x}+xsin(2x)

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

y^{^{''}} = x - y

y^{''}+y^'-12y=4,y(0)=0,y^'(0)=0

y^{^{''}} + y^{^{'}} - 12 y = 4, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 3 y^{^{'}} = x

Frequently Asked Questions (FAQ)

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