The solution of , ( dy dx ) = ax + by is - Vidyadip

MCQ

The solution of $\log \,\left( {\frac{{dy}}{{dx}}} \right) = ax + by$ is

A
$\frac{{{e^{by}}}}{b} = \frac{{{e^{ax}}}}{a} + c$
✓
$\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$
C
$\frac{{{e^{ - by}}}}{a} = \frac{{{e^{ax}}}}{b} + c$
D
None of these

✓

Answer

Correct option: B.

$\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$

b
(b) $\log \left( {\frac{{dy}}{{dx}}} \right) = ax + by$ ==> $\frac{{dy}}{{dx}} = {e^{ax + by}} = {e^{ax}}.{e^{by}}$

==> ${e^{ - by}}dy = {e^{ax}}dx$ ==> $\frac{{{e^{ - by}}}}{{ - b}} = \frac{{{e^{ax}}}}{a} + c$.

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