show that $(t) > $ Ct) for tocteti consider the differentiàl equations dt + P,(t)X = 0 CA) and P(t) dx1+ Q,c+) × = • dt (B) where P has a continuous derivative and is such that PE) > o, and Q and Q are Continuous and Such that Qz(t) > Q(t) astoat sb. let o be the solution of equatiba (A) Such that Ito) = c., $'tt») = <, , and let $ be the Sa lution of equation (B) such that ¢ (to) = C. and $'(to)=G where Co>o qud aso if Co =0. suppoje that (t) >o for to
show that $(t) > $ Ct) for tocteti consider the differentiàl equations dt + P,(t)X = 0 CA) and P(t) dx1+ Q,c+) × = • dt (B) where P has a continuous derivative and is such that PE) > o, and Q and Q are Continuous and Such that Qz(t) > Q(t) astoat sb. let o be the solution of equatiba (A) Such that Ito) = c., $'tt») = <, , and let $ be the Sa lution of equation (B) such that ¢ (to) = C. and $'(to)=G where Co>o qud aso if Co =0. suppoje that (t) >o for to
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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![show that $(t) > $ Ct) for tocteti
consider the differentiàl equations
dt
+ P(t)X = 0
CA)
and
P(t) dx1+ Q,c+) × = •
dt
(B)
where
P
has
a continuous derivative and is such that
PE) > o, and Q and Q are Continuous and Such that
Qz(t) > Q(t)
astoát sb. let ¢ be the solution of equatiba (A)
Such that lto) = c., $'(t.) = G, , and let $ be the
Sa lution of equation (B) such that ¢ (to) = C. and $'(to)=G
where Co>o qnd aso if Co =0. suppose that (t) >o tor
to <t<t,
on astsb. Ilet to and t be Such that
Hint: show that;
tor all te[a, b]. Thus show that the functibn
h such that h(t) = PE)/Q4) is increasing
For tostet, and objerve the value of h(to)
to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8afab3af-628d-46b8-8b41-1a4593a81072%2F3f336e7d-5ff5-418e-92a1-07e8e6bde1a5%2F08j606_processed.jpeg&w=3840&q=75)
Transcribed Image Text:show that $(t) > $ Ct) for tocteti
consider the differentiàl equations
dt
+ P(t)X = 0
CA)
and
P(t) dx1+ Q,c+) × = •
dt
(B)
where
P
has
a continuous derivative and is such that
PE) > o, and Q and Q are Continuous and Such that
Qz(t) > Q(t)
astoát sb. let ¢ be the solution of equatiba (A)
Such that lto) = c., $'(t.) = G, , and let $ be the
Sa lution of equation (B) such that ¢ (to) = C. and $'(to)=G
where Co>o qnd aso if Co =0. suppose that (t) >o tor
to <t<t,
on astsb. Ilet to and t be Such that
Hint: show that;
tor all te[a, b]. Thus show that the functibn
h such that h(t) = PE)/Q4) is increasing
For tostet, and objerve the value of h(to)
to
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