Given f(x) = 2x , f(2) = 1 , f(1) = 3 , find the particular solution to the differential equation.
- print Print
- list Cite
Expert Answers
briefcaseTeacher (K-12)
calendarEducator since 2011
write3,062 answers
starTop subjects are Math, Science, and Business
We are given f''(x)=2x, f'(2)=1, and f(1)=3 and we are asked to find the particular solution to the differential equation.
Since we know the second derivative, we can use the indefinite integral (or antidifferentiation) to find that `f'(x)=x^2+C` . C is called the constant of integration; we need it because a family of functions has the same derivative where the family of functions differ only by a constant.
Since we are given f'(2)=1, we can solve for C. Substituting 2 for x and...
(The entire section contains 272 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `f''(x) = 2, f'(2) = 5, f(2) = 10` Find the particular solution that satisfies the...
- 1 Educator Answer
- Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3
- 1 Educator Answer
- if f(x)=2x-3 and fg(x)=2x+1,find g(x)
- 1 Educator Answer
- Given f(x) = k(2+x), find the value of k if f^-1 (-2) = -3
- 1 Educator Answer
- `f(x) = (x^2 - 1)^3, [-1, 2]` Find the absolute maximum and minimum values of f on the...
- 1 Educator Answer