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)
MP
Answered by Matthew P. • Further Mathematics tutor
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