3. Two ordinary differential equations in terms of unknown functions u(x) and v(x) are given below. u′(x)−4u(x) = 2v(x)+2(ex+e−x) v′(x)+3v(x) = −5u(x) a. Show that the given first order ordinary differential equations above can be expressed as a second order ordinary differential equation as shown below: (show complete solution) u′′(x)−u′(x)−2u(x) = 8ex+4e−x

3. Two ordinary differential equations in terms of unknown functions u(x) and v(x) are given below. u′(x)−4u(x) = 2v(x)+2(ex+e−x) v′(x)+3v(x) = −5u(x) a. Show that the given first order ordinary differential equations above can be expressed as a second order ordinary differential equation as shown below: (show complete solution) u′′(x)−u′(x)−2u(x) = 8ex+4e−x

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 1CR

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Question

3. Two ordinary differential equations in terms of unknown functions u(x) and v(x) are given below.
u′(x)−4u(x) = 2v(x)+2(e^x+e^−x)
v′(x)+3v(x) = −5u(x)

a. Show that the given first order ordinary differential equations above can be expressed as a second order ordinary differential equation as shown below: (show complete solution)

u′′(x)−u′(x)−2u(x) = 8ex+4e−x

Expert Solution