Differential Equations Question 245
The general solution of the differential equation $ \frac{d^{2}y}{dx^{2}}=\cos x $ is
Options:
A) $ n^{2}y+\cos nx=n^{2}(Cx+D) $
B) $ n^{2}y-\sin nx=n^{2}(-Cx+D) $
C) $ n^{2}y+\cos nx=\frac{Cx+D}{n^{2}} $
D) None of these. [Where C and D are arbitrary constants]
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Answer:
Correct Answer: A
Solution:
The differential equation is $ \frac{d^{2}y}{dx^{2}}=\cos nx $ Integrating we get $ \frac{dy}{dx}=\frac{\sin nx}{n}+C_1 $
- (i) Integrating again $ y=-\frac{\cos nx}{n^{2}}+Cx+D $
$ \Rightarrow n^{2}y+\cos nx=n^{2}(Cx+D) $
BETA
