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### find general solution to: x(dy/dx) + 2y = 4x^2

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4(x^3)

Now integrate the entire equation and you get:        y(x^2) = |(4(x^3))dx = (x^4) + c

Divide through by (x^2) to get the general solution:

y = (x^2) + 4/(x^2)

1 year ago

Answered by Matthew, an A Level Further Mathematics tutor with MyTutor

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