Question #348537

y'' - 3y' - 10y = 0 ; y(0)=1 and y'(0)=10

Expert's answer

Corresponding (auxiliary) equation

"r_1=-2, r_2=5"

The general solution of the homogeneous differential equation is

"y(0)=c_1+c_2=1"

"y'=-2c_1e^{-2x}+5c_2e^{5x}"

"y'(0)=-2c_1+5c_2=10"

"c_1=-\\dfrac{5}{7}, c_2=\\dfrac{12}{7}"

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