A) \[\frac{7}{64}\]
B) \[\frac{13}{16}\]
C) \[\frac{49}{16}\]
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
\[\frac{dy}{dx}+\left( \frac{2}{x} \right)\,y\,=\,x\]is a Linerar D.E |
If \[{{e}^{\int{2/x/dx}}}={{x}^{2}}\] |
\[\therefore \] \[y\times {{x}^{2}}=\,\int{(x\times {{x}^{2}})dx}\] |
\[\Rightarrow \] \[y{{x}^{2}}=\,\frac{{{x}^{4}}}{4}+c\,and\,y\,(1)\,=\,1\] |
\[\Rightarrow \] \[c\,=\,\frac{3}{4}\] |
Put, \[x\,=\,\frac{1}{2}\,\text{then},\]\[y\,=\,\frac{49}{16}.\] |
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