MHT CET · Maths · Differential Equations
The order and degree of a differential equation obtained by eliminating arbitrary constant \(C\) from the family of curves \(y^2=2 C(x+\sqrt{C})\) are respectively
- A 1,3
- B 1,4
- C 1,1
- D 1,2
Answer & Solution
Correct Answer
(A) 1,3
Step-by-step Solution
Detailed explanation
from (i) and (ii)
\(\begin{aligned} & y^2=2 y \frac{\mathrm{d} y}{\mathrm{~d} x}\left(x+\sqrt{y \frac{\mathrm{d} y}{\mathrm{~d} x}}\right) \\ & \Rightarrow y-2 x \frac{\mathrm{d} y}{\mathrm{~d} x}=2 \frac{\mathrm{d} y}{\mathrm{~d} x} \cdot \sqrt{y \cdot \frac{\mathrm{d} y}{\mathrm{~d} x}} \\ & \Rightarrow\left(y-2 x \frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2=4 y\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^3 \text { order }=1, \text { degree }=3\end{aligned}\)
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