Solve : y''2 + y' - 6y = 0
Answer & explanation
Correct answer: option 1
Put d/dx = D
D2y + Dy - 6y = 0
D2 + D - 6 = 0
D2 +3D - 2D - 6 = 0
D(D+3) -2(D+3) = 0
D=-3,2
for D=-3 ⇒ d/dx=-3
dy/dx=-3y
dy/y=-3dx
ln y=-3x
y=e-3x
Similarly, solve for D=2.
Solve : y''2 + y' - 6y = 0
Correct answer: option 1
Put d/dx = D
D2y + Dy - 6y = 0
D2 + D - 6 = 0
D2 +3D - 2D - 6 = 0
D(D+3) -2(D+3) = 0
D=-3,2
for D=-3 ⇒ d/dx=-3
dy/dx=-3y
dy/y=-3dx
ln y=-3x
y=e-3x
Similarly, solve for D=2.