Question:
For the differential equation $x \frac{dy}{dx}+2y=xy \frac{dy}{dx}$,
For the differential equation $x \frac{dy}{dx}+2y=xy \frac{dy}{dx}$,
Updated On: Jul 6, 2022
- order is $1$ and degree is $1$
- solution is $ln(yx^2) = C - y$
- order is $1$ and degree is $2$
- solution is $ln(xy^2) = C + y$
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The Correct Option is A
Solution and Explanation
Given, $x \frac{dy}{dx}\left(1-y\right)+2y=0$
$\Rightarrow \left(\frac{1-y}{y}\right)dy+2 \frac{dx}{x}=0$
$\Rightarrow ln\,y-y+2\,ln\,x=C$
$\Rightarrow ln\left(yx^{2}\right)=C+y$
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Concepts Used:
Differential Equations
A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on.
Orders of a Differential Equation
First Order Differential Equation
The first-order differential equation has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as: dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.
Types of Differential Equations
Differential equations can be divided into several types namely
- Ordinary Differential Equations
- Partial Differential Equations
- Linear Differential Equations
- Nonlinear differential equations
- Homogeneous Differential Equations
- Nonhomogeneous Differential Equations