Q. 33.7( 3 Votes )

Solve the following equations:


Answer :

Given differential equation can be written as:


……(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 one side we get,




We know that:



Integrating on both sides, we get,



log(v2 + 1) = -logx + logC ( LogC is an arbitrary constant)


Since y = vx,


we get



( )


Applying exponential on both sides, we get,




Cross multiplying on both sides we get,


y2 + x2 = Cx


The solution for the given differential equation is y2 + x2 = Cx.


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