Let m and n be the order and the degree of the differential equation whose solution is y = cx + c² - 3c^3/2 + 2, where c is a parameter. Then,

m = 1, n = 4

$\frac{d y}{d x}=c \Rightarrow$ the differential equation is ;

$y=x . \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^2-3 .\left(\frac{d y}{d x}\right)^{3 / 2}+2$

Clearly its order is one and degree 4.

Hence (1) is the correct answer.