Exercise
$\frac{dx}{dt}+2tx^3+\frac{x}{t}=0$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dx/dt+2tx^3x/t=0. Rewrite the differential equation. We identify that the differential equation \frac{dx}{dt}+\frac{x}{t}=-2tx^3 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 3. Simplify.
Solve the differential equation dx/dt+2tx^3x/t=0
Final answer to the exercise
$x=\frac{1}{\sqrt{\left(\ln\left(t^{4}\right)+C_0\right)t^{2}}},\:x=\frac{-1}{\sqrt{\left(\ln\left(t^{4}\right)+C_0\right)t^{2}}}$