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Popular Calculus >

x^{''}+ax=b

Solution

x^{^{''}} + a x = b

Solution

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

Solution steps

x^{''} (t) + a x = b

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}+6y^'+9y=12e^t

2y^{''}+8y^'+80y=1,y(0)=0,y^'(0)=0

D(x)=sqrt(82.5-2*5x)

y^{''}-y^'-6y=12cos(3x)

Frequently Asked Questions (FAQ)

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