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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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sirm3dBest ResponseYou've already chosen the best response.1
\[\Large {y=c_1e^{4x}+c_2e^{2x}e^{3x}+e^{x}/9\\1=c_1+c_21+1/9}\] \[\Large {y'=4c_1e^{4x}+2c_2e^{2x}+3e^{3x}e^{x}/9\\0=4c_1+2c_2+31/9}\] solve the unknowns \(\large c_1,\;c_2\)
 one year ago

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