Solve the differential equation:  dydx=5xy

This is a first order linear homogeneous differential equation. We can solve it using the method of separation of variables. Here are the steps:

1. Rewrite the differential equation: dy/dx = 5xy
2. Separate the variables: dy/y = 5x dx
3. Integrate both sides: ∫dy/y = ∫5x dx
4. The left side becomes ln|y| and the right side becomes (5/2)x^2 + C
5. So, ln|y| = (5/2)x^2 + C
6. Exponentiate both sides to solve for y: |y| = e^(5/2)x^2 + C
7. Remove the absolute value by considering the positive and negative solutions: y = ±e^(5/2)x^2 + C

So the general solution to the differential equation dy/dx = 5xy is y = ±e^(5/2)x^2 + C.