- #1

kreil

Gold Member

- 668

- 68

I am new to integration so I am unsure about my work on this problem.

[tex]\frac{dy}{dx}=x{\sqrt{y}}[/tex]

[tex]dy=(dx)(x)(\sqrt{y})[/tex]

[tex]\frac{dy}{\sqrt{y}}=(dx)(x)[/tex]

[tex]\int{\frac{dy}{\sqrt{y}}}=\int{(x)(dx)}[/tex]

[tex]2y^{\frac{1}{2}}=\frac{1}{2}x^2+ C[/tex]

[tex]10=\frac{9}{2}+C[/tex]

[tex]C=\frac{11}{2}[/tex]

[tex]2y^{\frac{1}{2}}=\frac{1}{2}x^2+\frac{11}{2}[/tex]

[tex]y=(\frac{1}{4}x^2+\frac{11}{4})^2[/tex]

If I did it correctly, is there an easier way to do it? If I messed up, where?

Thanks