Q.216. Differential Equation.

Question 216.
If y = e^x sin 3x, then prove that
d^2y/dx^2 - 2 dy/dx + 10y =0.

Answer 216.
y = e^x sin3x
=> dy/dx
= e^x sin3x + 3e^x cos3x
= y + 3e^x cos3x ... (1)

=> d^2y/dx^2
= dy/dx + 3e^x cos3x - 9e^x sin3x ... (2)

Plugging 3e^x cos3x = dy/dx - y from (1) in (2) and e^x sin3x = y
=> d^2y/dx^2 = dy/dx + dy/dx - y - 9y
=> d^2y/dx^2 - 2dy/dx + 10y = 0.

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