A) \[y'={{y}^{2}}\]
B) \[y''=y'y\]
C) \[yy''=y'\]
D) \[yy''={{(y')}^{2}}\]
Correct Answer: D
Solution :
\[y={{c}_{1}}{{e}^{{{c}_{2}}x}}\] ?(i) \[y'={{c}_{1}}{{c}_{2}}{{e}^{{{c}_{2}}x}}\] \[y'={{c}_{2}}y\] ?.. (from (i)] ?(ii) \[y''={{c}_{2}}y'\] ?(iii) from (ii) & (iii) \[\frac{y'}{y}=\frac{y''}{y'}\Rightarrow yy''={{(y')}^{2}}\]
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