- #1
snowJT
- 117
- 0
Homework Statement
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. Homework Statement
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?