Show that `y=b e^x+c e^(2x)\ ` is a solution of the differential equation `(d^2y)/(dx^2)-3(dy)/(dx)+2y=0.`

Explanation

Given, `y=b e^x+c e^(2x)`` \ \ \ ...(i)`


Differentiating w.r.t `x`


`y'=b e^x+2c e^(2x)`` \ \ \ ...(ii)`


Differentiating w.r.t `x`


`y''=b e^x+4c e^(2x)`` \ \ \ ...(iii)`



`LHS= y''-3y+2y`


`=b e^x+4c e^(2x)-3(b e^x+2c e^(2x))+2(b e^x+c e^(2x))`


`=b e^x+4c e^(2x)-3b e^x-6c e^(2x)+2b e^x+2c e^(2x)`


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