Final Answer
Step-by-step Solution
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Group the terms of the differential equation. Move the terms of the $v$ variable to the left side, and the terms of the $t$ variable to the right side of the equality
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$\frac{3}{\left(v^3-1\right)v}dv=\frac{2t}{1+t^2}dt$
Learn how to solve differential equations problems step by step online. Solve the differential equation (3(1+t^2)dv)/dt=2tv(v^3-1). Group the terms of the differential equation. Move the terms of the v variable to the left side, and the terms of the t variable to the right side of the equality. Simplify the expression \frac{3}{\left(v^3-1\right)v}dv. Integrate both sides of the differential equation, the left side with respect to v, and the right side with respect to t. Take out the constant 2 from the integral.