Question

The degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{\frac{2}{3}}+4-3\frac{d^{2}y}{d{x}^2}+5\frac{dy}{dx}=0$ is -

• A. $1$
• B. $2$
• C. $3$
• D. None of these

Answer 1

The correct option is B $2$

$(\frac{d^{3}y}{{dx}^3}{)}^{\frac{2}{3}}+4-3\frac{d^{2}y}{{dx}^2}+5\frac{dy}{dx}=0$

$(\frac{d^{3}y}{{dx}^3}{)}^{\frac{2}{3}}=-4+3\frac{d^{2}y}{{dx}^2}-5\frac{dy}{dx}$

$((\frac{d^{3}y}{{dx}^3}{)}^{\frac{2}{3}}{)}^3=(-4+3\frac{d^{2}y}{{dx}^2}-5\frac{dy}{dx}{)}^3$

$((\frac{d^{3}y}{{dx}^3}{)}^{}{)}^2=(-4+3\frac{d^{2}y}{{dx}^2}-5\frac{dy}{dx}{)}^3$

The power of $\frac{d^{3}y}{{dx}^3}$ is 2.

Hence , degree of the differential equation is 2.