Brief Calculus.

Question

Solve the following Initial Value Problems

Find f(x) if f' (x) = 10e^2x+ 5 and f(0) = 3

Answer 1

f(x) = ∫10e^2x+5dx = 5e^2x +5x + C

f(0) = 3 = 5+C

C=-2

f(x) = 5e^2x+5x-2