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Differential equations
Nature of the roots
MCQ
For the equation y'' - 6y' + 9y = 0, what is the form of the general solution?
Possible answers
y
=
C
1
e
3
x
+
C
2
e
−
3
x
y = C_1 e^{3x} + C_2 e^{-3x}
y
=
C
1
e
3
x
+
C
2
e
−
3
x
y
=
(
C
1
+
C
2
x
)
e
3
x
y = \left(C_1 + C_2 x\right)e^{3x}
y
=
(
C
1
+
C
2
x
)
e
3
x
y
=
C
1
cos
(
3
x
)
+
C
2
sin
(
3
x
)
y = C_1 \cos(3x) + C_2 \sin(3x)
y
=
C
1
cos
(
3
x
)
+
C
2
sin
(
3
x
)
y
=
C
1
e
3
x
+
C
2
x
e
−
3
x
y = C_1 e^{3x} + C_2 x e^{-3x}
y
=
C
1
e
3
x
+
C
2
x
e
−
3
x
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