Find y in terms of x for the equation 2x(dy/dx) + 4y = 8x^2
divide through by 2x to get: dy/dx + 2y/x = 4x this is now in the form of dy/dx + P(x)y = Q(x)
intergrating factor = exp( integral(P(x)) dx ) = exp( integral(2/x) dx ) = exp( 2 ln(x) ) = x2
therefore d( (x2)y )/dx = 4 x3 -> (x2)y = integral ( 4x^3 ) dx = x4
therefore y = x2
TE
Answered by Tom E. • Further Mathematics tutor
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