Exercise
$\frac{dx}{dt}=\frac{t+5}{x^3}$
Step-by-step Solution
Learn how to solve polynomial factorization problems step by step online. Solve the differential equation dx/dt=(t+5)/(x^3). Group the terms of the differential equation. Move the terms of the x variable to the left side, and the terms of the t variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to x, and the right side with respect to t. Expand the integral \int\left(t+5\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the integral \int x^3dx and replace the result in the differential equation.
Solve the differential equation dx/dt=(t+5)/(x^3)
Final answer to the exercise
$x=\sqrt[4]{4\left(\frac{t^2}{2}+5t+C_0\right)},\:x=-\sqrt[4]{4\left(\frac{t^2}{2}+5t+C_0\right)}$