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 variables on same side we get,






We know that:


and


Also,



Integrating on both sides, we get,





Since y = vx, we get,






()




( alogx = logxa)




The solution for the given Differential equation is


6