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**dif. eq. problem -- dont know why it is wrong**

Solve for y: [tex]x \frac{dy}{dx} + 6y=5x[/tex]

with y(1)=2

[tex]\frac{dy}{dx} =5 - 6\frac{y}{x} [/tex]

[tex]\frac{6y}{x} \frac{dy}{dx} =5[/tex]

[tex] 3y^2=\frac{5}{2}x^2 +C[/tex]

[tex] y= \sqrt{\frac{5x^2}{6}+\frac{C}{3}}[/tex]

solve for when y(1)=2

[tex]4=\frac{5}{6}+\frac{C}{3}[/tex]

[tex]C=\frac{19}{2}[/tex]

so..

[tex]y= \sqrt{\frac{5x^2}{6}+\frac{19}{6}}[/tex]

what did i do wrong? because this is not the answer

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