The general solution of {d^{2} y}/{d x^{2}}-6 \frac{d y}{d x}+9 y=0 is

Correct Answer is : y=(C1+C2x)e3x

{C}_{1} {e}^{3 {x}}+ {C}_{2} {e}^{-3 {x}}

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 25 of 65

Marks: +1, -0

The general solution of

\;{d^{2} y}/{d x^{2}}-6 \;{d y}/{d x}+9 y=0

Solution:

{D}^{2}-6 {D}+9=0

⇒( {D}-3)^{2}=0

{D}=3,3 → \;\text " equal roots "\;

∴ {y}=( {c}_{1}+ {c}_{2}) {e}^{3 {x}}

Go to Question:

Prev Question

Next Question