SOLUTION: A. Let g(t) be the solution of the initial value problem 4t(dy/dt)+y=0, t>0, with g(1)=1. Find g(t). g(t)= My answer is t^(-1/4), is correct. B. Let f(t) be the solution of

Algebra ->  Expressions -> SOLUTION: A. Let g(t) be the solution of the initial value problem 4t(dy/dt)+y=0, t>0, with g(1)=1. Find g(t). g(t)= My answer is t^(-1/4), is correct. B. Let f(t) be the solution of      Log On


   



Question 1184045: A. Let g(t) be the solution of the initial value problem
4t(dy/dt)+y=0, t>0,
with g(1)=1.
Find g(t).
g(t)= My answer is t^(-1/4), is correct.
B. Let f(t) be the solution of the initial value problem
4t(dy/dt)+y=t^4
with f(0)=0.
Find f(t).
f(t)= My answer is 1/4t^(1/3), it's wrong
C. Find a constant c so that
k(t)=f(t)+cg(t)
solves the differential equation in part B and k(1)=14.
c=

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
B. The answer is y+=+f%28t%29+=+t%5E4%2F17. This satisfies the IV condition of f(0) = 0, and the D.E., as
.

C. k%28t%29+=+f%28t%29+%2B+cg%28t%29+=+t%5E4%2F17+%2B+ct%5E%28-1%2F4%29 ===> k%281%29+=+1%2F17+%2B+c1%5E%28-1%2F4%29+=+1%2F17%2B+c+=+14
===> c+=+237%2F17