dy/dx = 4ye^(5x)

Question

a) Separate the differential equation, then integrate both sides.

b) Write the general solution as a function y(x).

For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate differential equations and/or integrate both sides...

Answer 1

dy / y = 4 e^(5x) dx

ln y = (4/5) e^(5x) + c

e^ln y = y = e^ [(4/5)e^(5x) +c)

y = e^c e^[(4/5)e^(5x) ]

y = C e^[(4/5)e^(5x) ]