The solution to the differential equation is:
[tex]g(x) = x^2*sgn(x)[/tex]
We want to solve:
g'(x) = 2*|x|
If we integrate g(x), we will get:
[tex]\int\limits {2*|x|} \, dx[/tex]
Remember that:
Then:
[tex]g(x) = \int\limits {2*|x|} \, dx = 2*(\frac{x^2}{2}*sgn(x)) + C[/tex]
Where sgn(x) is the sign of the value x, and C is a constant of integration.
We also know that g(0) = 0, then:
[tex]g(0) = 2*(\frac{0^2}{2}*sgn(0)) + C = C = 0[/tex]
So we conclude that C = 0.
Then the function is:
[tex]g(x) = x^2*sgn(x)[/tex]
If you want to learn more about differential equations, you can read:
https://brainly.com/question/18760518
