A. Let g(t) be the solution of the initialvalue problemdy4t-+у %3D 0, t> 0,dtwith g(1) = 1.Find g(t).g(t) =B. Let f(t) be the solution of the initial valueproblemdy4ty = 7?dtwith f(0) = 0.Find f(t).f(t) =C. Find a constant c so thatk(t) = f(t) + cg(t)%3Dsolves the differential equation in part B andk(1) = 8.с —

we are given two initial value problems. A) 4tdydt+y=0,t>0whose solution is g(t) , g(1)=1and…

Answered: A. Let g(t) be the solution of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A. Let g(t) be the solution of the initial
value problem
dy
4t-
+у %3D 0, t> 0,
dt
with g(1) = 1.
Find g(t).
g(t) =
B. Let f(t) be the solution of the initial value
problem
dy
4t
y = 7?
dt
with f(0) = 0.
Find f(t).
f(t) =
C. Find a constant c so that
k(t) = f(t) + cg(t)
%3D
solves the differential equation in part B and
k(1) = 8.
с —

Expert Solution

Step 1

we are given two initial value problems.

A) $4 t \frac{d y}{d t} + y = 0, t > 0 w h o s e s o l u t i o n i s g (t), g (1) = 1 a n d 4 t \frac{d y}{d t} + y = t^{2} w h o s e s o l u t i o n i s f (t) a n d f (0) = 0$

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