Question

The order and degree of the differential equation.
${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+\left(\frac{dy}{dx}\right)=\int ydx$ are respectively.

• A. $2$ and $3$
• B. $2$ and $2$
• C. $3$ and $1$
• D. $3$ and $2$

Answer 1

The correct option is C $3$ and $1$

differentiating the given equation on both sides

we get

$\frac{d}{dx}(\frac{d^{2}y}{d{x}^2}{)}^3+\frac{d}{dx}(\frac{dy}{dx})=\frac{d}{dx}(\int ydx)$

$3(\frac{d^{2}y}{d{x}^2}{)}^2\times \frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}=y$

therefore the order is $3$ and the degree is $1$[since degree is the power of highest order]