the variation of parameters method, and the general solution. No conditions are given. Normally what constants you use are arbitrary, but for grading purposes use A as the coefficient for cosine and B as the coefficient for sine in your general solution. The Wroskian W(cos x, sin x) u(x)= v(x)= 1 1 cos The general solution is y (x) A-cos(x) +B sin(x)
the variation of parameters method, and the general solution. No conditions are given. Normally what constants you use are arbitrary, but for grading purposes use A as the coefficient for cosine and B as the coefficient for sine in your general solution. The Wroskian W(cos x, sin x) u(x)= v(x)= 1 1 cos The general solution is y (x) A-cos(x) +B sin(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Show that the inhomogeneous equation y" + y = xe-2x, has the homogeneous solutions y₁ = cos x and y₂ = sin x. (Plug them in and show they check. Notice this problem has the same homogeneous equation as another assigned problem.) Find the Wronskian for this pair of solutions, determine the functions u(x) and v(x)
the variation of parameters method, and the general solution. No conditions are given.
Normally what constants you use are arbitrary, but for grading purposes use A as the coefficient for cosine and B as the coefficient for sine in your general solution.
The Wroskian W(cos x, sin x) =
u(x)=
v(x)=
1
The general solution is
y (x)= A-cos(x) + B-sin(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8e0ad34-47bd-4edd-8e64-7fbb4be3cef6%2Fba75d330-ca64-4db8-9814-4de7bc50782e%2F3vwbehn_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the inhomogeneous equation y" + y = xe-2x, has the homogeneous solutions y₁ = cos x and y₂ = sin x. (Plug them in and show they check. Notice this problem has the same homogeneous equation as another assigned problem.) Find the Wronskian for this pair of solutions, determine the functions u(x) and v(x)
the variation of parameters method, and the general solution. No conditions are given.
Normally what constants you use are arbitrary, but for grading purposes use A as the coefficient for cosine and B as the coefficient for sine in your general solution.
The Wroskian W(cos x, sin x) =
u(x)=
v(x)=
1
The general solution is
y (x)= A-cos(x) + B-sin(x)
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