dy -3+5 y dt

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter57: Fundamental Geometric Constructions
Section: Chapter Questions
Problem 6A
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Solve for the General/particular solution given in the problem.

For the first picture.

The second picture is how you must solve the first picture.

dr
1.
ニ-4rt
when t=0,r=r,
dt
solution:
dr
-4rt
-
dt
dr
-4t dt
separation of variables
dr
= S -4tdt+C
v integrating both sides
r
Inr=-4
simplification
ニー
-2²+C
r=e
v substitution
r=e2.e°,let e=A
-2t
r=Ae
@t=0,r=r,
General Solutions
ro=Ae-2(0))
A=r,,therefore
v using boundary condition
- 2t
Particular solutions
r=r,e-
Transcribed Image Text:dr 1. ニ-4rt when t=0,r=r, dt solution: dr -4rt - dt dr -4t dt separation of variables dr = S -4tdt+C v integrating both sides r Inr=-4 simplification ニー -2²+C r=e v substitution r=e2.e°,let e=A -2t r=Ae @t=0,r=r, General Solutions ro=Ae-2(0)) A=r,,therefore v using boundary condition - 2t Particular solutions r=r,e-
dy
=3+5y
dt
Transcribed Image Text:dy =3+5y dt
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