An ordinary differential equation is given below \(6\frac{{{d^2}y}}{{d{x^2}}} + \frac{{dy}}{{dx}} - y = 0\) The general solution of the above equation (with constants C1 and C2), is

\(y\left( x \right) = \;{C_1}x{e^{ - \frac{x}{3}}} + {C_2}{e^{\frac{x}{2}}}\)

\(y\left( x \right) = \;{C_1}{e^{ - \frac{x}{3}}} + {C_2}{e^{\frac{x}{2}}}\)

\(y\left( x \right) = \;{C_1}{e^{\frac{x}{3}}} + {C_2}{e^{ - \frac{x}{2}}}\)

\(y\left( x \right) = \;{C_1}{e^{ - \frac{x}{3}}} + {C_2}x{e^{\frac{x}{2}}}\)

An ordinary differential equation is given below \(6\frac{{{d^2}y}}{{d

1.	An ordinary differential equation is given below \(6\frac{{{d^2}y}}{{d{x^2}}} + \frac{{dy}}{{dx}} - y = 0\) The general solution of the above equation (with constants C1 and C2), is
A.	\(y\left( x \right) = \;{C_1}{e^{ - \frac{x}{3}}} + {C_2}{e^{\frac{x}{2}}}\)
B.	\(y\left( x \right) = \;{C_1}{e^{\frac{x}{3}}} + {C_2}{e^{ - \frac{x}{2}}}\)
C.	\(y\left( x \right) = \;{C_1}x{e^{ - \frac{x}{3}}} + {C_2}{e^{\frac{x}{2}}}\)
D.	\(y\left( x \right) = \;{C_1}{e^{ - \frac{x}{3}}} + {C_2}x{e^{\frac{x}{2}}}\)
Answer» C. \(y\left( x \right) = \;{C_1}x{e^{ - \frac{x}{3}}} + {C_2}{e^{\frac{x}{2}}}\)

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