the general solution by finding the homogeneous solution and a particular solution.   1) y" + y = 6(e^x) + 3 and the correct answer is y = c1*cos(x) + c2*sin(x) + 3(e^x) + 3. can you please show me how to get to the correct answer?

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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 10E
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find the general solution by finding the homogeneous solution and a particular solution.

 

1) y" + y = 6(e^x) + 3

and the correct answer is y = c1*cos(x) + c2*sin(x) + 3(e^x) + 3. can you please show me how to get to the correct answer?

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,