Part 3. Two ordinary differential equations in terms of unknown functions m(x) and 1(x) are given below. - m'(x) — 5m(x) = 31(x) + 3(e* + e¯×) l'(x) + 4l(x) = -6m(x) 3A. Show that the given first order ordinary differential equations above can be expressed as a second order ordinary differential equation as shown below: m" (x) — m'(x) — 2m(x) = = 15e* +9e-* HINT: You can start your solution by differentiating the first equation with respect to x. 3B. Determine the general solution of the ODE given in [3A]. Use ONLY the method of variation of parameters. 3C. If m(0) = -0.50, and m' (0) = -2.5, determine the value of m(ln2).
Part 3. Two ordinary differential equations in terms of unknown functions m(x) and 1(x) are given below. - m'(x) — 5m(x) = 31(x) + 3(e* + e¯×) l'(x) + 4l(x) = -6m(x) 3A. Show that the given first order ordinary differential equations above can be expressed as a second order ordinary differential equation as shown below: m" (x) — m'(x) — 2m(x) = = 15e* +9e-* HINT: You can start your solution by differentiating the first equation with respect to x. 3B. Determine the general solution of the ODE given in [3A]. Use ONLY the method of variation of parameters. 3C. If m(0) = -0.50, and m' (0) = -2.5, determine the value of m(ln2).
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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![Part 3. Two ordinary differential equations in terms of unknown functions m(x) and 1(x)
are given below.
m'(x) — 5m(x) = 31(x) + 3(e* + e¯*)
l'(x) + 41(x) = −6m(x)
3A. Show that the given first order ordinary differential equations above can be expressed
as a second order ordinary differential equation as shown below:
m" (x) — m'(x) — 2m(x) : = 15e* +9e-x
HINT: You can start your solution by differentiating the first equation with respect to x.
3B. Determine the general solution of the ODE given in [3A]. Use ONLY the method of
variation of parameters.
3C. If m(0) = -0.50, and m' (0) = -2.5, determine the value of m(In2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9443130a-9efe-42d5-ae4a-6434bc102ab0%2F30af534b-e969-4f6e-a2a8-1838c9d15848%2Fng25bmq_processed.png&w=3840&q=75)
Transcribed Image Text:Part 3. Two ordinary differential equations in terms of unknown functions m(x) and 1(x)
are given below.
m'(x) — 5m(x) = 31(x) + 3(e* + e¯*)
l'(x) + 41(x) = −6m(x)
3A. Show that the given first order ordinary differential equations above can be expressed
as a second order ordinary differential equation as shown below:
m" (x) — m'(x) — 2m(x) : = 15e* +9e-x
HINT: You can start your solution by differentiating the first equation with respect to x.
3B. Determine the general solution of the ODE given in [3A]. Use ONLY the method of
variation of parameters.
3C. If m(0) = -0.50, and m' (0) = -2.5, determine the value of m(In2).
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