MCQ
વિકલ સમીકરણ $\frac{{dy}}{{dx}} + ay = {e^{mx}}$ નો ઉકેલ મેળવો.
- A$(a + m)\,y = {e^{mx}} + c$
- B$y{e^{ax}} = m{e^{mx}} + c$
- C$y = {e^{mx}} + c{e^{ - ax}}$
- ✓$(a + m)y = {e^{mx}} + c{e^{ - ax}}(a + m)$
$\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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