How can I solve a nonlinear DE with a constant using partial fractions?

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The discussion focuses on solving the nonlinear differential equation dx/dt = x^2 - cx, where c is a constant. The equation is identified as separable, allowing for integration using partial fractions. The recommended approach involves rewriting the left side as dx/(x(x-c)) and integrating to find the solution. This method effectively simplifies the problem and leads to a clear path for solving the differential equation.

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Hi, what kind of technic should i use to solve the below DE?

dx/dt=x^2-cx, where c is just a constant.

Many thanks
 
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ksquare said:
Hi, what kind of technic should i use to solve the below DE?

dx/dt=x^2-cx, where c is just a constant.

Many thanks
That's trivially separable. Integrate
\frac{dx}{x(x-c)}= dt
using "partial fractions" for the left side.
 

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