anonymous
  • anonymous
Find a particular solution of y"+y=2e^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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helpmeplease
  • helpmeplease
Use the annihilator method on the 2e^x. Think, what differential operator would result in the answer.
anonymous
  • anonymous
is there a formula i can follow? this is supposed to be a non homogeneous second order differential equation.
helpmeplease
  • helpmeplease
Well, 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.

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anonymous
  • anonymous
(e^x)"+(e^x)=2e^x
helpmeplease
  • helpmeplease
D-1 = Ae^(1x) yp = Ae^(1x) e^x = Ae^x+A^ex = 2e^x
helpmeplease
  • helpmeplease
sorry, function, not e^x
helpmeplease
  • helpmeplease
also, use t for 1.
helpmeplease
  • helpmeplease
I 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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