Question:
A homogenous differential equation of the form \(\frac{dy}{dx}=h(\frac{x}{y})\) can be solved by making the substitution
A homogenous differential equation of the form \(\frac{dy}{dx}=h(\frac{x}{y})\) can be solved by making the substitution
Updated On: Sep 6, 2023
\(y=vx\)
\(v=yx\)
\(x=vy\)
\(x=v\)
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The Correct Option is C
Solution and Explanation
The correct answer is C:\(x=vy\)
For solving the homogenous equation of the form \(\frac{dx}{dy}=h(\frac{x}{y})\),we need to make the substitution as \(x=vy\)
Hence,the correct answer is C.
For solving the homogenous equation of the form \(\frac{dx}{dy}=h(\frac{x}{y})\),we need to make the substitution as \(x=vy\)
Hence,the correct answer is C.
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Concepts Used:
Homogeneous Differential Equation
A differential equation having the formation f(x,y)dy = g(x,y)dx is known to be homogeneous differential equation if the degree of f(x,y) and g(x, y) is entirely same. A function of form F(x,y), written in the formation of kn F(x,y) is called a homogeneous function of degree n, for k≠0. Therefore, f and g are the homogeneous functions of the same degree of x and y. Here, the change of variable y = ux directs to an equation of the form;
dx/x = h(u) du which could be easily desegregated.
To solve a homogeneous differential equation go through the following steps:-
Given the differential equation of the type
