Question

Form the differential equation of y=ae3xcos⁡(x+b) Where y′=dydx and yn=d2ydx2?

• A. (A) y′′−6y′+10y=0
• B. (B) y′′−6y′−10y=0
• C. (C) y′′+6y′−10y=0
• D. (D) y′′+6y′+10y=0

Answer 1

Answer: (C)

(C) y′′+6y′−10y=0

Answer 2

Explanation:
Given,y=ae3xcos⁡(x+b)There are two constants a and b so differentiate two times Differentiating wr.t x,We get,y′=3ae3xcos⁡(x+b)−ae3xsin⁡(x+b)⇒y′=3y−ae3xsin⁡(x+b)⇒ae3xsin⁡(x+b)=3y−y′Differentiating again w.r.t x,We get,3ae3xsin⁡(x+b)+ae3xcos⁡(x+b)=3y′−y′′⇒3(3y−y′)+y−3y′−yn=0⇒9y−3y′+y−3y′−yn=0⇒y′′+6y′−10y=0Hence, the correct option is (C).