Q. 75.0( 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:




-log(1-v2) = logx + logC


log(1-v2)-1 = log(Cx)


( alogx = logxa)


( loga + logb = logab)



Applying exponential on both sides, we get,



Since y = vx, we get,







Cross multiplying on both sides we get,


x = C(x2 – y2)


The solution for the given Differential equation is x = C(X2-y2)


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