Mathematics I (Calculus) - Old Questions

11. Find the solution of y" + 6y′ + 9 = 0, y(0) = 2, y(0) = 1.

Given

The characteristics equation of given differential equation is

Here the roots are real and equal.

The general solution is

Now, applying the condition y(0)=2

Again, 

Then, 

Applying the condition y’(0)=1

The particular solution of the given equation is