With c as arbitrary constant the solution of the differential equation dy/dx=ky is
Question
With c as arbitrary constant the solution of the differential equation is
Solution
The solution to the differential equation dy/dx = ky is y = Ce^(kt), where C is an arbitrary constant.
Here are the steps to solve it:
- Separate the variables: dy/y = k dx.
- Integrate both sides: ∫dy/y = ∫k dx.
- Apply the integral: ln|y| = kx + C1.
- Solve for y: y = e^(kx+C1).
- Simplify the equation: y = Ce^(kt), where C = e^C1 is an arbitrary constant.
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