The degree of the differential equation whose solution is $y^2=8 a(x+a)$, is
The degree of the differential equation whose solution is $y^2=8 a(x+a)$, is
2
1
4
3
Solution
We have $y^2=8 a x+8 a^2$
Differentiating w.r.t. $\mathrm{x}$, we get
$2 y \frac{d y}{d x}=8 a \quad \Rightarrow \quad a=\left(\frac{y}{4}\right) \frac{d y}{d x}$
Substituting value of ' $a$ ' in eq. (1), we get
$\begin{aligned}
& y^2=8\left(\frac{y}{4}\right) \frac{d y}{d x}(x)+8\left[\left(\frac{y}{4}\right)\left(\frac{d y}{d x}\right)\right]^2=2 x y \frac{d y}{d x}+\left(\frac{y^2}{2}\right)\left(\frac{d y}{d x}\right)^2 \\
& \therefore 2 y^2=4 x y\left(\frac{d y}{d x}\right)+y^2\left(\frac{d y}{d x}\right)^2
\end{aligned}$
Hence order $=1$, degree $=2$