Find the general solution of the homogeneous differential equation {eq}\displaystyle y'=\frac{x+y}{x-y}. {/eq}
Question:
Find the general solution of the homogeneous differential equation {eq}\displaystyle y'=\frac{x+y}{x-y}. {/eq}
Homogeneous Differential Equations:
There are many types of differential equations, but the homogeneous differential equation is the one of the type {eq}g(x,y) dx=f(x,y) dy {/eq}, where {eq}f {/eq} and {eq}g {/eq} are homogeneous functions of the same power of {eq}x {/eq} and {eq}y {/eq}. To find the general equation of these differential equations, we substitute {eq}y=vx {/eq}. Then the expression is simplified and solved further, and later on, the value of {eq}v=\frac{y}{x} {/eq} is put back in the solution.
Answer and Explanation: 1
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View this answer{eq}y'=\frac{x+y}{x-y}\\ Putting~...
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Chapter 15 / Lesson 2Explore the separation of variables in differential equations. Study the steps involved in the method of separation of variables with examples in each step.