Q. 95.0( 1 Vote )

# Solve the following equations: Given Differential equation is:  ……(1)

Homogeneous equation: A equation is said to be homogeneous if f(zx,zy) = znf(x,y) (where n is the order of the homogeneous equation).

Let us assume     f(zx,zy) = z0f(x,y)

So, given differential equation is a homogeneous differential equation.

We need a substitution to solve this type of linear equation and the substitution is y = vx.

Let us substitute this in (1) We know that       Bringing like on the same side we get,   We know that Integrating on both sides we get,  ( logC is an arbitrary constant)

log(1-2v2) = -4logx + 4logC

log(1–2v2) = -logx4 + logC4

( xloga = logax) ( )

Applying exponential on both sides we get, Since y = vx, we get,     Cross multiplying on both sides we get,

x2(x2–2y2) = c4

x4–2x2y2 = c4

The solution for the given differential equation is x4–2x2y2 = C4.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Interactive Quiz on DIfferential CalculusFREE Class  Functional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 