The number of arbitrary constants that appear | vedclass

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

Question

(A) To find the number of arbitrary constants in the general solution of a differential equation, we need to determine the order of the differential e

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) To find the number of arbitrary constants in the general solution of a differential equation, we need to determine the order of the differential equation. The number of arbitrary constants is equal to the order of the differential equation.First, we rewrite the given equation to remove the fractional exponent:$\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$Squaring both sides, we get:$\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^3 = 25 \left(\frac{d^3 y}{d x^3}\right)^2$The highest order derivative present in the equation is $\frac{d^4 y}{d x^4}$, which is of order $4$.Since the order of the differential equation is $4$, the general solution will contain $4$ arbitrary constants.

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

Similar Questions

If $y=a^3 e^{b^2 x+c}$ is the general solution of a differential equation,where $a$ and $c$ are arbitrary constants and $b$ is a fixed constant,then the order of the differential equation 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:

The order and degree of the differential equation $e^{\frac{d^2 y}{d x^2}} = x$ are . . . . . . respectively.

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

If $m$ is the order and $n$ is the degree of the differential equation $y = \frac{dp}{dx} + \sqrt{a^2 p^2 - b^2}$,where $p = \frac{dy}{dx}$,then the value of $m+n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module