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anonymous
 3 years ago
Does anyone know how to solve this?
Solve the differential equation by variation of parameters, subject to the initial conditions
y(0) = 1, y'(0) = 0.
y'' + 2y' − 8y = 5e^(−3x) − e^(−x)
I get y = c1e^(4x)+c2e^(2x)e^(3x)+e^(x)/9 but idk how to carry on with the initial condition part.
anonymous
 3 years ago
Does anyone know how to solve this? Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. y'' + 2y' − 8y = 5e^(−3x) − e^(−x) I get y = c1e^(4x)+c2e^(2x)e^(3x)+e^(x)/9 but idk how to carry on with the initial condition part.

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\Large {y=c_1e^{4x}+c_2e^{2x}e^{3x}+e^{x}/9\\1=c_1+c_21+1/9}\] \[\Large {y'=4c_1e^{4x}+2c_2e^{2x}+3e^{3x}e^{x}/9\\0=4c_1+2c_2+31/9}\] solve the unknowns \(\large c_1,\;c_2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks. I was able to solve the unknowns. \[c_{1} = \frac{ 121 }{ 54 } , c_{2} = \frac{ 7 }{54 }\] Is that what you got as well?
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