Q. 105.0( 1 Vote )

Solve the following equations:


Answer :

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 x = vy.


Let us substitute this in (1)



We know that:







Bringing like variables on the same side we get,



We know that ∫exdx = ex + C and



Integrating on both sides, we get,



ev = logy + C


Since x = vy, we get



The solution for the given Differential equation is .


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 Calculus50 mins
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