Answer:
[tex]y=4e^{-(x+1)}[/tex] will be the solutions.
Step-by-step explanation:
The given equation is [tex]y=C_{1}e^{x}+C_{2}e^{-x}[/tex]
Therefore, for x = -1
[tex]4=C_{1}e^{-1}+C_{2}e^{1}[/tex] ------(1)
Now y'(-1) = -4
y'(x) = [tex]C_{1}e^{x}-C_{2}e^{-x}[/tex] = -4
[tex]C_{1}e^{-1}-C_{2}e^{1}[/tex] = -4 -----(2)
By adding equation (1) and (2)
[tex]2C_{1}e^{-1}=0[/tex]
[tex]C_{1}=0[/tex]
From equation (1),
[tex]4=0+C_{2}e^{1}[/tex]
[tex]C_{2}=4e^{-1}[/tex]
By placing the values in the parent equation
y = [tex]4e^{-1}\times e^{-x}[/tex]
y = [tex]4e^{-(x+1)}[/tex]
