Question

solve the following differential equation
f''(x)=2 , f'(1)=4 , f(2) =-2

Answer 1

f''(x) = 2

int(f''(x)) = int(2) ... Integrate both sides

f'(x) = 2x + C

Since f'(1) = 4, we can say

4 = 2(1) + C

4 = 2 + C

2 = C

C = 2

So f'(x) = 2x + 2


f'(x) = 2x+2

int(f'(x)) = int(2x+2)

f(x) = x^2 + 2x + C

Because f(2) = -2, we know that

-2 = (2)^2 + 2(2) + C

-2 = 4 + 4 + C

-2 = 8 + C

-10 = C

C = -10

So f(x) = x^2 + 2x - 10

Answer 2

thank you

Answer 3

sure thing

Answer 4

I loved how explained it to me lol