Solution of differential equation dy dx + ay = e^ mx is - Vidyadip

MCQ

Solution of differential equation $\frac{{dy}}{{dx}} + ay = {e^{mx}}$ is

A
$(a + m)\,y = {e^{mx}} + c$
B
$y{e^{ax}} = m{e^{mx}} + c$
C
$y = {e^{mx}} + c{e^{ - ax}}$
✓
$(a + m)y = {e^{mx}} + c{e^{ - ax}}(a + m)$

✓

Answer

Correct option: D.

$(a + m)y = {e^{mx}} + c{e^{ - ax}}(a + m)$

d
(d) $I.F.$ $ = {e^{\int_{}^{} {a\,dx} }} = {e^{ax}}$

$\therefore $Required solution is given by

$y.\,{e^{ax}} = \int_{}^{} {{e^{mx}}.{e^{ax}}} dx = \frac{{{e^{(a + m)x}}}}{{a + m}} + C$

==> $y = \frac{{{e^{mx}}}}{{a + m}} + C{e^{ - ax}}$

==> $y(a + m) = {e^{mx}} + C(a + m){\rm{ }}{e^{ - ax}}$.

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