Anti-Derivatives or integrals

Question

Find the function y(x) if y'(x)=3.4⋅e^x−4.4⋅sin(x)

and y(0)=0.1

Answer 1

y = f(x) = 3.4* e^x + 4.4*cos(x) + C

(0, 1/10) = (0, 0.1)

1/10 = 3.4*e^(0) + 4.4* cos(0) + C

1/10 = 3.4 * 1 + 4.4 * 1 + C

1/10 = 3.4 + 4.4 + C

0.1 = 7.8 + C

C = -7.7

the function solution is y = f(x) = 3.4* e^x + 4.4*cos(x) - 7.7