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Popular Calculus >

(d^2+1)y=e^x

Solution

(d^{2} + 1) y = e^{x}

Solution

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

Solution steps

(d^{2} + 1) y = e^{x}

Solve linear ODE:

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

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

Graph

Popular Examples

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

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

y^{''}=2y^'+15y+sin(3t)

y^{''}-6y^'+8y=-2e^{2t}

y^{''}-2y^'-17y=sin(t)-cos(t)

Frequently Asked Questions (FAQ)

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