Q. If $\frac{d^{2}y}{dx^{2}}\sin{x = 0}$, then the solution of differential equation is
A) $y = \sin{x + cx + d}$
B) $y = \cos{x + cx^{2} + d}$
C) $y = \tan{x + c}$
D) $y = \log{\sin{x + cx}}$
Explanation
(a)
The given equation can be rewritten as, $\frac{d^{2}y}{dx^{2}} = - \sin x$.
On integrating the given equation
$\int_{}^{}{\frac{d^{2}y}{dx^{2}}dx =}\int_{}^{}{- \sin{x\ dx + c}}$
$\Rightarrow \ \frac{dy}{dx} = - ( - \cos{x) + c = \cos{x + c}}$
Again, on integrating, we get
$\int_{}^{}{\frac{dy}{dx}dx =}\int_{}^{}{\cos{x\ dx + \int_{}^{}{c\ dx + d}}}$
$y = \sin{x + cx + d}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.