Two ordinary differential equations in terms of unknown functions u(x) and v(x) are given below. u′(x)−5u(x) = 3v(x)+3(ex+e−x) v′(x)+4v(x) = −6u(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) = 15ex+9e−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)−5u(x) = 3v(x)+3(ex+e−x) v′(x)+4v(x) = −6u(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) = 15ex+9e−x b.) Determine the general solution of the ODE given above. Use ONLY the method of variation of parameters.
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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Two ordinary differential equations in terms of unknown functions u(x) and v(x) are given below.
u′(x)−5u(x) = 3v(x)+3(ex+e−x)
v′(x)+4v(x) = −6u(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) = 15ex+9e−x
b.) Determine the general solution of the ODE given above. Use ONLY the method of variation of parameters.
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