Differential Equation

Hello

Can anyone hp me with this question:

Find the general solution to the differential equation

dy/dx = 5xy

Thanks

dy/dx = 5xy

This is separable, so separate and integrate:

dy = 5xy dx
(1/y) dy = 5x dx
∫ (1/y) dy = 5 ∫ x dx
ln(y) = (5/2)x^2 + C
y = e^[(5/2)x^2 + C]
y = [e^C][e^((5/2)x^2)] <-- Since e^C is just another constant, replace it by C:

y = C[e^[(5/2)x^2]]

Done!