MCQ
Solution of differential equation $x\frac{{dy}}{{dx}} = y + {x^{^2}}$ is
- A$y = {\log _e}x + \frac{{{x^2}}}{2} + a$
- B$y = \frac{{{x^3}}}{3} + \frac{a}{x}$
- ✓$y = {x^2} + ax$
- DNone of these
$\therefore $ Solution is $y \cdot \frac{1}{x} = \int_{}^{} {x \cdot \frac{1}{x}dx} $
==> $\frac{y}{x} = x + a$ ==> $y = {x^2} + ax$.
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$\left| {\begin{array}{*{20}{c}}
{{{\log }_e}\,a_1^ra_2^k}&{{{\log }_e}\,a_2^ra_3^k}&{{{\log }_e}\,a_3^ra_4^k} \\
{{{\log }_e}\,a_4^ra_5^k}&{{{\log }_e}\,a_5^ra_6^k}&{{{\log }_e}\,a_6^ra_7^k} \\
{{{\log }_e}\,a_7^ra_8^k}&{{{\log }_e}\,a_8^ra_9^k}&{{{\log }_e}\,a_9^ra_{10}^k}
\end{array}} \right| = 0$
Then the number of elements in $S$, is