1. The problem statement, all variables and given/known data This is my first big differential equation that I have solved by myself, and I wanted to see if it is correct done, or what I have done wrong with it. Would really appreciate if somebody could take a look on it. y''+6y'+8y=0 when y(0)=1 and y'(0)=0 3. The attempt at a solution This is my solution y''+6y'+8y=0 r2+6r+8=0 r=-3+- sqrt (9-8)= sqrt 1 r1= -2 r2= -4 y=Ce-2x+De-4x y'=-2Ce-2x-4De-4x y(0)=1 1=Ce0+De0=C+D y'(0)=0 0=-2Ce0-4De0=-2C-4D 1=C+D 0=-2C-4D I take 1=C+D and take -D on both sides so I get 1-D=C I take 0=-2C-4D and take +2 on both sides so I get 2=C-4D I now put in 1-D in it, and get 2=1-D-4D and that I can change to 3=-5D I then take +5 on both sides and i get that 8=D I go back to 1-D=C and I get that C=-7 I now take C and D and put them in the equation, so I get: -7e-2x+8e-4x Is this right, or have I made something wrong on the way?