(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Solve the differential equation

dy/dx = x(y^{2}+3)/y

b) Find the unique function y(x) satisfying the differential equation with initial

condition

dy/dx = x^{2}y, y(1) = 1

2. Relevant equations

3. The attempt at a solution

With question a) I am no entirely sure but I have done

dy/dx = x(y^{2}+3)/y

Let u = y^{2}+3/y

So dy/dx = x.u

Integral of (dy/dx) = Integral (x.u)

y = x^{2}u^{2}/2

Then sub it back in. I'm not entirely sure

With question b) I have done

dy/dx = x^{2}y

dy . 1/y = x^{2}dx

integral of(1/y dx) = x^{3}/3 + c

Ln y = x^{3}/3 + c

I am not sure if I am on the right track,

I would appreciate any help.

Thanks

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# Homework Help: Differential/Integration equation manipulation

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