The discussion centers on solving the differential equation dx/dt = t/(x*t^2 + x^3) using the substitution u = t^2. A participant corrects the initial substitution, clarifying that the equation transforms to dx/du = 1/(2(xu + x^3)). The conclusion reached is that the problem can be simplified using an integrating factor, indicating that it is a linear differential equation. This approach allows for a straightforward solution process.
PREREQUISITESStudents, mathematicians, and engineers who are working with differential equations, particularly those interested in solving linear equations and applying substitution methods.
No, you don't obtain that equation. If u= t^2, then dx/dt= dx/du du/dt=2t dx/du.nocloud said:i have this equation:
dx/dt = t/(x*t^2+x^3)
using the substitution u = t^2, i obtain the following equation:
du/dx = 2u/(ux+x^3)
does anybody know how i can solve this equation?