solusi persamaan umum (5x+6x kuadrat) dy/dx= 3x kuadrat +7

[tex]\displaystyle (5x+6x^2)\frac{dy}{dx}=3x^2+7\\\frac{dy}{dx}=\frac{3x^2+7}{5x+6x^2}\\\frac{dy}{dx}=\frac{3x^2+7}{6x^2+5x}\cdot\frac22\\\frac{dy}{dx}=\frac{6x^2+14}{2(6x^2+5x)}\\\frac{dy}{dx}=\frac{6x^2+5x-5x+14}{2(6x^2+5x)}\\\frac{dy}{dx}=\frac12-\frac{5x-14}{2x(6x+5)}\\\frac{dy}{dx}=\frac12\left(1-\frac{5x-14}{x(6x+5)}\right)\\\frac{dy}{dx}=\frac12\left(1-\frac{14}{5}\cdot\frac{1}{x}-\frac{109}{5}\cdot\frac{1}{6x+5}\right)[/tex]
[tex]\displaystyle dy=\frac12\left(1-\frac{14}{5}\cdot\frac{1}{x}-\frac{109}{5}\cdot\frac{1}{6x+5}\right)\,dx\\\int dy=\int\frac12\left(1-\frac{14}{5}\cdot\frac{1}{x}-\frac{109}{5}\cdot\frac{1}{6x+5}\right)\,dx\\y=\frac12\left(x-\frac{14}{5}\cdot\ln|x|-\frac{109}{5}\cdot\frac{1}{6}\ln|6x+5|\right)+C\\\boxed{\boxed{y=\frac12x-\frac{7}{5}\cdot\ln|x|-\frac{109}{60}\ln|6x+5|+C}}[/tex]