The differential equation left[frac{1+left(fr | vedclass

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

Question

(A) Given the differential equation: $\left[\frac{1+\left(\frac{dy}{dx}\right)^2}{\left(\frac{d^2y}{dx^2}\right)^{\frac{3}{2}}}\right]^2 = kx$ First,s

Vedclass · Accepted Answer

order $= 2$,degree $= 3$

Vedclass · Answer

(A) Given the differential equation: $\left[\frac{1+\left(\frac{dy}{dx}\right)^2}{\left(\frac{d^2y}{dx^2}\right)^{\frac{3}{2}}}\right]^2 = kx$ First,simplify the expression by removing the fractional exponent: $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^2}{\left(\frac{d^2y}{dx^2}\right)^3} = kx$ Now,multiply both sides by $\left(\frac{d^2y}{dx^2}\right)^3$: $\left[1+\left(\frac{dy}{dx}\right)^2\right]^2 = kx \left(\frac{d^2y}{dx^2}\right)^3$ The order of a differential equation is the highest derivative present,which is $\frac{d^2y}{dx^2}$,so the order is $2$. The degree is the power of the highest derivative when the equation is expressed as a polynomial in derivatives,which is $3$. Therefore,the order is $2$ and the degree is $3$.

The differential equation $\left[\frac{1+\left(\frac{dy}{dx}\right)^2}{\left(\frac{d^2y}{dx^2}\right)^{\frac{3}{2}}}\right]^2 = kx$ is of

Similar Questions

If $m$ is the order and $n$ is the degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2-1$,then:

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

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:

If $c_1, c_2, c_3, c_4, c_5$ are arbitrary constants,then the order of the differential equation whose general solution is $y=(c_1+c_2) \sin (x+c_3)+c_4 e^{x+c_5}$ is

For the differential equation $\frac{d^3 y}{d x^3}=0$,$y=a x^2+b x+c$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module