Find the general solution of the differential | vedclass

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

Question

(A) The given differential equation is $y dx - (x + 2y^2) dy = 0$. Dividing by $dy$,we get $y \frac{dx}{dy} - x - 2y^2 = 0$. Rearranging the terms,we

Vedclass · Accepted Answer

$x = 2y^2 + Cy$

Vedclass · Answer

(A) The given differential equation is $y dx - (x + 2y^2) dy = 0$. Dividing by $dy$,we get $y \frac{dx}{dy} - x - 2y^2 = 0$. Rearranging the terms,we have $y \frac{dx}{dy} - x = 2y^2$. Dividing by $y$,we get $\frac{dx}{dy} - \frac{1}{y} x = 2y$. This is a linear differential equation of the form $\frac{dx}{dy} + P_1 x = Q_1$,where $P_1 = -\frac{1}{y}$ and $Q_1 = 2y$. The integrating factor $(I.F.)$ is given by $I.F. = e^{\int P_1 dy} = e^{\int -\frac{1}{y} dy} = e^{-\log y} = e^{\log(y^{-1})} = \frac{1}{y}$. The general solution is given by $x(I.F.) = \int (Q_1 	imes I.F.) dy + C$. Substituting the values,we get $x \cdot \frac{1}{y} = \int (2y \cdot \frac{1}{y}) dy + C$. $\frac{x}{y} = \int 2 dy + C$. $\frac{x}{y} = 2y + C$. $x = 2y^2 + Cy$.

Find the general solution of the differential equation $y dx - (x + 2y^2) dy = 0$.

Similar Questions

The solution of the differential equation $(y^{2}+2x) \frac{dy}{dx}=y$ satisfies $x=1, y=1$. Then the solution is

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

Let the solution curve $y = y(x)$ of the differential equation $\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1+x^6)^{3/2}} y = 2x \exp \left( \frac{x^3 - \tan^{-1}(x^3)}{\sqrt{1+x^6}} \right)$ pass through the origin. Then $y(1)$ is equal to:

Let $y(x)$ be the solution of the differential equation $(x \log x) \frac{dy}{dx} + y = 2x \log x$,$(x \ge 1)$. Then $y(e)$ is equal to: $[y(1) = 0]$

Let $y=y(x)$ be the solution of the differential equation $\operatorname{cosec}^{2} x \, dy + 2 \, dx = (1+y \cos 2x) \operatorname{cosec}^{2} x \, dx$,with $y(\frac{\pi}{4})=0$. Then,the value of $(y(0)+1)^{2}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module