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$y = {e^{mx}} + c{e^{ - ax}}$
- ✓$(a + m)y = {e^{mx}} + c{e^{ - ax}}(a + m)$
$\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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The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).
Let Z = px + qy, where p.q > 0.
Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is: