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Model Paper 2 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 21 Mark
Question
What are the order and degree respectively of the differential equation whose solution is $y=c x+c^2-3 c^{3 / 2}+2$ where c is a parameter?
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Answer

Given, $y=c x+c^2-3 c^{3 / 2}+2....(i)$
On differentiating both sides w.r.t. x, we get
$\frac{d y}{d x}= C ...(ii)$ From Eqs. $(i)$ and $(ii)$, we have
$ y=\frac{d y}{d x} \times x+\left(\frac{d y}{d x}\right)^2-3\left(\frac{d y}{d x}\right)^{3 / 2}+2$
$\Rightarrow y-x \frac{d y}{d x}-\left(\frac{d y}{d x}\right)^2-2=-3\left(\frac{d y}{d x}\right)^{3 / 2}$
$\Rightarrow\left[y-x\left(\frac{d y}{d x}\right)-\left(\frac{d y}{d x}\right)^2-2\right]^2=9\left(\frac{d y}{d x}\right)^3 $
Hence, order is $1$ and degree is $4 $.

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