If a and b are respectively the order and deg | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the differential equation: $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$. To find the degree,we must eliminate the fra

Vedclass · Accepted Answer

$b = 3a$

Vedclass · Answer

(C) Given the differential equation: $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$. To find the degree,we must eliminate the fractional exponent of the derivative. Rearranging the equation: $y^2(y^{\prime \prime})^2 + x^2y^2 - \sin x = -3x(y^{\prime})^{1/3}$. Cubing both sides to remove the power of $1/3$: $(y^2(y^{\prime \prime})^2 + x^2y^2 - \sin x)^3 = (-3x)^3(y^{\prime}) = -27x^3(y^{\prime})$. The highest order derivative present is $y^{\prime \prime}$,so the order $a = 2$. The highest power of the highest order derivative after making the equation a polynomial in derivatives is $2 	imes 3 = 6$. Thus,the degree $b = 6$. Comparing $a = 2$ and $b = 6$,we get $b = 3a$.

If $a$ and $b$ are respectively the order and degree of the differential equation $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$,then:

Similar Questions

The degree of the differential equation $\log \left(\frac{dy}{dx}\right) = (2x + 3\frac{dy}{dx})^2$ is

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}}-4 \frac{dy}{dx}-7x=0$ are respectively.

The degree of the differential equation ${\left( {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right)^{3/4}} = {\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{1/3}}$ is

The order and degree of the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$ are respectively:

Which of the following equations is non-linear?

Vedclass Test Series

Exam Paper Generator

Online Exam Module