Y(t) = a exp(2t) + b exp(5t) <img src="-f-y(0)-20-3D-202-20-3Cbr-20-2F-3E.jpg"> and <img src="-f-y'(0)-20-3D-203-20-3Cbr-20-2F-3E.jpg"> Find…

Question

`y(t) = a exp(2t) + b exp(5t)`


and

Find a and b. I did the substitutions and everything and got
and
but apparently this is not right

Answer 1

`y(0)=2\implies 2=ae^(2(0))+be^(5(0))\implies 2=a+b`


`y'(t)=2ae^(2t)+5be^(5t)`

`y'(0)=3\implies 3=2ae^(2(0))+5be^(5(0))\implies 3=2a+5b`

Solving this should yield
`a=\frac73` and
`b=-\frac13`.