Question

The order and degree of the differential equation whose solution is $y=cx+c^2-3c^{3/2}+2$, where $c$ is a parameter, is

• A. order = 4, degree = 4
• B. order = 4, degree = 1
• C. order = 1, degree = 4
• D. None of these

Answer 1

Answer: (C)

$y=ex+c^2{-}_{}3c^{3/2}+2...\left(i\right)$
Differentiating above with respect to x, we get $\frac{dy}{dx}=c$.
Putting this value of c in $\left(i\right)$, we get
$y=x\frac{dy}{dx}+{\left(\frac{dy}{dx}\right)}^2-{\left(\frac{dy}{dx}\right)}^{3/2}+2$
Clearly its order is ONE and after removing the fractional power we get the degree FOUR.