A) first order and second degree
B) first order and first degree
C) second order and first degree
D) second order and second degree
Correct Answer: C
Solution :
The given equation is\[A{{x}^{2}}+B{{y}^{2}}=1\] On differentiating w:r.t. x, we get \[2Ax+2By\frac{dy}{dx}=0\] ...(i) Again differentiating, we get \[2A+2B\left\{ {{\left( \frac{dy}{dx} \right)}^{2}}+y\frac{{{d}^{2}}y}{d{{x}^{2}}} \right\}=0\] ??..(ii) On solving Eqs. (i) and (ii), we get \[y\frac{{{d}^{2}}y}{d{{x}^{2}}}+{{\left( \frac{dy}{dx} \right)}^{2}}-\frac{y}{x}.\frac{dy}{dx}=0\] This is the required differential equation whose order is 2 and degree is 1.
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