A) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{y}^{2}}=0\]
B) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{a}^{2}}y=0\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+a{{y}^{2}}=0\]
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-{{a}^{2}}y=0\]
Correct Answer: B
Solution :
Solution is \[y={{c}_{1}}\cos ax+{{c}_{2}}\sin ax\] Differentiate it w.r.t. x, we get \[\frac{dy}{dx}=-{{c}_{1}}a\sin ax+{{c}_{2}}a\cos ax\] Again \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-{{c}_{1}}{{a}^{2}}\cos ax-{{c}_{2}}{{a}^{2}}\sin ax\] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-{{a}^{2}}({{c}_{1}}\cos ax+{{c}_{2}}\sin ax)\Rightarrow \frac{{{d}^{2}}y}{d{{x}^{2}}}=-{{a}^{2}}y\] or \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{a}^{2}}y=0\].
You need to login to perform this action.
You will be redirected in
3 sec
