Solved Differential Equation

Topic : Differential Equation

Question : If y = A . Cos x - B . Sin x and prove d²y/dx² + y = 0

Solution :
y = A . Cos x - B . Sin x
Differentiate with respect to x
dy/dx = - A . Sin x - B . Cos x
d²y/dx² = - A . Cos x - B .(- Sin x)
d²y/dx² = - A . Cos x + B . Sin x
d²y/dx² = - (A . Cos x - B . Sin x)
d²y/dx² = -y (because y = A . Cos x - B . Sin x)
and d²y/dx² + y= 0 Thus proved