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

Obtain the general solution of [tex]2xydy - 6y^2dy + 8xdx + y^2dx = 0[/tex]

2. The attempt at a solution

[tex]2xydy - 6y^2dy + 8xdx + y^2dx = 0[/tex]

[tex]2xydy + y^2dx = 6y^2dy - 8xdx[/tex]

[tex]\intd(xy^2) = \int6y^2dy - 8xdx[/tex]

[tex]xy^2 = \frac{6y^3}{3} - \frac{8x^2}{2}+C[/tex]

[tex]xy^2 = 2y^3 - 4x^2+C[/tex]

3. The problem statement, all variables and given/known data

Find the particular solution of the DE that satisfies the condition y = 5 when x = 1

4. The attempt at a solution

[tex]xy^2 = 2y^3 - 4x^2+C[/tex]

[tex](5)^2 = 2(5)^3 - 4+C[/tex]

[tex]25 = 250 - 4+C[/tex]

[tex]C = -221[/tex]

Does all of this look right to you? I'm not so sure about the last part?

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# Integratable combination question

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