Q. 135.0( 2 Votes )

Solve the following differential equations :


Answer :

Here, 2xydx + ( x2 + 2y2 ) dy = 0



It is a homogeneous equation


Put y = vx


And


So,







Integrating Both Sides we get,


…… (1)





1 + 2v2 = A – 2Av2 + Bv2 + cv


1 + 2v2 = v2( – 2A + B) + cv + A


Comparing the coefficients of like power of v,


A = 1


C = 0


– 2A + B = 2


– 2 + B = 2


B = 4




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