Final answer to the problem
$y=\sqrt{C_2e^{3x^2}+\frac{1}{3}},\:y=-\sqrt{C_2e^{3x^2}+\frac{1}{3}}$
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Step-by-step Solution
Learn how to solve integration techniques problems step by step online. Solve the differential equation ydy+xdx=3xy^2dx. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x\cdot dx from both sides of the equation. Factor the polynomial 3xy^2dx-x\cdot dx by it's greatest common factor (GCF): x\cdot dx. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Final answer to the problem
$y=\sqrt{C_2e^{3x^2}+\frac{1}{3}},\:y=-\sqrt{C_2e^{3x^2}+\frac{1}{3}}$
