Q. 85.0( 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 y = vx.


Let us substitute this in (1)



We know that






Bringing like variables on same side we get,





We know that:


and


Also,



Integrating on both sides, we get,




( log C is an arbitrary constant)



( alogx = logxa)



( loga + logb = logab)


Since y = vx,


we get,






Applying exponential on both sides we get,




The solution of the 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 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