Solved Differential Equation

Topic : Differential Equation

Problem : If y = 4 Sin 3x prove y" + 9y = 0

Solution :
y = 4 Sin 3x
differentiate with respect to x
y' = 4 Cos 3x . 3
y' = 12 Cos 3x
Again differentiate with respect to x
y" = 12 (- Sin 3x . 3)
y" = - 36 Sin 3x

Now consider y" + 9y = 0
Substitute the value of y and y"
-36 Sin 3x + 9(4 Sin 3x)
-36 Sin 3x + 36 Sin 3x = 0
Hence proved