The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e}^{5x}},\]where A and B are arbitrary constants, is [MNR 1988]

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\]

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+8\frac{dy}{dx}+15y=0\]

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+15y=0\]

The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e

1.	The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e}^{5x}},\]where A and B are arbitrary constants, is [MNR 1988]
A.	\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+8\frac{dy}{dx}+15y=0\]
B.	\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+15y=0\]
C.	\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\]
D.	None of these
Answer» C. \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}+y=0\]

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The differential equation of the family of curves \[y=A{{e}^{3x}}+B{{e}^{5x}},\]where A and B are arbitrary constants, is [MNR 1988]

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