$$\frac{dx}{dt} + x^2 = B + A\cdot e^{C\ln\big(\frac{x}{x_0}\big)+\ln(x_0)}, \quad x(t_0)=x_0$$
Can anyone please help me where I can start from this equation?
I simplified a complicated equation and I am currently stuck.
I looked back at my differential equation textbook and could not find a single formula to solve it. Most of the formula that I am seeing are function of $t$ but in this equation is $x$.
Please help to start with something.
Hint... You can simplify the exponential term and write the equation as
$$ \frac{dx}{dt} = -x^2 + B + A x_0 \left(\frac{x}{x_0}\right)^C, $$
which is a separable variable DE. However the method of solution will depend on the value of $C$.