Final answer to the problem
$y=\sqrt{2\left(\frac{3x^2}{2}+3x+C_0\right)},\:y=-\sqrt{2\left(\frac{3x^2}{2}+3x+C_0\right)}$
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Step-by-step Solution
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy/dx=(3(x+1))/y. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression 3\left(x+1\right)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(3x+3\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$y=\sqrt{2\left(\frac{3x^2}{2}+3x+C_0\right)},\:y=-\sqrt{2\left(\frac{3x^2}{2}+3x+C_0\right)}$
