What are the order and degree respectively of the differential equation whose solution is $\mathrm{y}=\mathrm{cx}+\mathrm{c}^2-3 \mathrm{c}^{3 / 2}+2$, where c is a parameter?

Given : Solution of differential equation is $y=c x+c^2-3 c^{\frac{3}{2}}+2$...(1) To find order and degree of differential equation, we will find differential equation first. Now differentiating equation (1) w.r.t. $x$ and putting value of $c$ to remove it, we get $\frac{d y}{d x}=c$ $\begin{aligned} & y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^2-3\left(\frac{d y}{d x}\right)^{\frac{3}{2}}+2 \\ & \Rightarrow(y-2)^2+\left(\frac{d y}{d x}\right)^4+(2 x-9)\left(\frac{d y}{d x}\right)^3\end{aligned}$ $+\left(x^2-2 y+4\right)\left(\frac{d y}{d x}\right)^2+(-2 x y+4 x) \frac{d y}{d x}=0$ Hence order of differential equation is 1 and degree is 4 .