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anonymous
 5 years ago
Find a particular solution of y"+y=2e^x
anonymous
 5 years ago
Find a particular solution of y"+y=2e^x

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helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0Use the annihilator method on the 2e^x. Think, what differential operator would result in the answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is there a formula i can follow? this is supposed to be a non homogeneous second order differential equation.

helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0Well, you need to use the differential operator concept. What D would destroy 2e^x? Then use that differential operator and create the particular solution. Then plug that solution into the function, and see what the coefficient is.

helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0D1 = Ae^(1x) yp = Ae^(1x) e^x = Ae^x+A^ex = 2e^x

helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, function, not e^x

helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0also, use t for 1.

helpmeplease
 5 years ago
Best ResponseYou've already chosen the best response.0I mangled that a little bit. Your y_p = Ae^x. You have to determine what A is. To do that, substitute the y_p back into the function, and solve for A.
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