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Mathematics Question on Derivatives

The solution of x2d2ydx2+x+dydx+y=sin⁡(log⁡x2)x ^2 \frac{d^2y}{dx^2}+x+\frac{dy}{dx}+y=\sin(\log x^2).

A

y=Acos(logx)+Bsin(log.x)−13sin(logx2)y = Acos (logx) + Bsin(log.x)-\frac{1}{3}sin(logx^2)

B

y=Acos(logx2)+Bsin(log.x2)+13sin(logx)y = Acos (logx^2) + Bsin(log.x^2)+\frac{1}{3}sin(logx)

C

y=Acos(logx)−Bsin(log.x)+13cos(logx)y = Acos (logx) - Bsin(log.x)+\frac{1}{3}cos(logx)

D

y=Acos(logx2)−Bsin(log.x2)−13cos(logx2)y = Acos (logx^2) - Bsin(log.x^2)-\frac{1}{3}cos(logx^2)

Answer

y=Acos(logx)+Bsin(log.x)−13sin(logx2)y = Acos (logx) + Bsin(log.x)-\frac{1}{3}sin(logx^2)

Explanation

Solution

The correct option is (A):y=Acos(logx)+Bsin(log.x)−13sin(logx2)y = Acos (logx) + Bsin(log.x)-\frac{1}{3}sin(logx^2) .