| 1. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\] |
| 2. \[{{\left( \frac{dy}{dx} \right)}^{2}}+\frac{dy}{dx}=0\] |
| Select the correct answer using the code given below. |
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Correct Answer: A
Solution :
[a] \[y=2\cos x+3\sin x\] \[\frac{dy}{dx}=-2\sin x+3\cos x;\frac{{{d}^{2}}y}{dx}=-2\cos x-3\sin x\] \[=-(2cosx+3sinx)=-y;\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]
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