I assume the equation is

since separating variables leads to


for which the condition that
is actually relevant, as opposed to the simpler differential equation

(though it's a bit more work to solve for
in this case)
That the slope
is non-zero tells us that

Integrate both sides.

On the left, expand into partial fractions.


With the given initial value, we find

so the particular solution is

By definition of absolute value, with the initial condition of
and the condition
, we can remove the absolute values.

Solve for
.



Then

On the off-chance you meant the other equation I suggested, we find



Solving for
involves picking the right branch of the cube root that agrees with
. With the cube root formula, we find

where
![\xi = \frac{2\sqrt[3]{4}}{\sqrt[3]{3x^2 - 3 + √(9x^4 - 18x^2 - 1015)}}](https://img.qammunity.org/2023/formulas/mathematics/college/vk6cpjdjtzvnrgx1iovglmzjomrv13dboa.png)
With a calculator, we find
