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)

$y = ex + c^{2}- _{ }3c^{3/2}+2\quad...\left(i\right)$
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.