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: (HINT: You can start your solution by differentiating the first equation with respect to x.) u′′(x)−u′(x)−2u(x) = 8ex+4e−x b.) Determine the general solution of the ODE given above. Use ONLY the method of variation of parameters.
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: (HINT: You can start your solution by differentiating the first equation with respect to x.) u′′(x)−u′(x)−2u(x) = 8ex+4e−x b.) Determine the general solution of the ODE given above. Use ONLY the method of variation of parameters.
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
Related questions
Question
3. Two ordinary
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: (HINT: You can start your solution by differentiating the first equation with respect to x.)
u′′(x)−u′(x)−2u(x) = 8ex+4e−x
b.) Determine the general solution of the ODE given above. Use ONLY the method of variation of parameters.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 8 steps with 9 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,