Question

Laplace transform: y"+4y=-2cost, y(0)=-3, y'(0)=1

Answer 1

y"+4y=-2cost, y(0)=-3, y'(0)=1

y" + 4y = - 2 cost

Take the Laplace transform of everything and plug in the initial conditions.

solving for Y(s) and combining into a single term

doing the partial fractions on this. First get the partial fraction decomposition.​​​​​​​

Now, setting numerators equal gives,​​​​​​​

Now, comparing coefficients,

Now, substituting the above values we get,:

Taking inverse transformation,

​​​​​​​