The differential equation x' = 2*x^(1/2) is separable and can be solved by rewriting it as dx/(2*x^(1/2)) = dt. Integrating both sides yields the general solution, which includes a constant of integration. While the solution x = t^2 satisfies the equation, the complete solution provided by Wolfram is 1/4 (4t^2 + 4tC + C^2), which accounts for the integration constant. Understanding the integration process is crucial for deriving the complete solution.
PREREQUISITESStudents studying differential equations, educators teaching calculus, and anyone seeking to deepen their understanding of solving first-order separable differential equations.
This DE is separable. Write it aspergradus said:Homework Statement
I have the differential equation:
x' = 2*x1/2
The Attempt at a Solution
I can see easily that the solution x = t2 satisfies the equation, however wolfram tells me the solution is:
1/4 (4 t2 + 4 t C + C2)
which also satisfies the solution... I'm wondering how do I solve this differential equation in order to get the solution Mathematic got?