у" + 25у %3D 0, у(0) 3 6, у'(0) 3D —4 Y(x) = | 5 cos( 5x) – sin(5x) sin (5x) x

We have given differential equation

y"+25y=0

with initial conditions y(0) =6, y'(0) =-4

We have to find solution using, 

step 1. Find indicial equation. 

Step 2. Find roots. 

Step 3. Find general solution. 

Step 4. Using initial conditions find the value of constants. 

Step 5. Substitute