Differential Equations - Study Mode
[#11] The solution of differential equation $$frac{{{{ ext{d}}^2}{ ext{u}}}}{{{ ext{d}}{{ ext{x}}^2}}} - { ext{K}}frac{{{ ext{du}}}}{{{ ext{dx}}}} = 0$$ xa0 xa0where K is constant, subjected to boundary conditions u(0) = 0 and u(L) = U is
Correct Answer
(B) $${ ext{u}} = { ext{U}}left[ {frac{{1 - {{ ext{e}}^{{ ext{Kx}}}}}}{{1 - {{ ext{e}}^{{ ext{KL}}}}}}}
ight]$$
[#12] A solution of the following differential equation is given by $$frac{{{{ ext{d}}^2}{ ext{y}}}}{{{ ext{d}}{{ ext{x}}^2}}} - 5frac{{{ ext{dy}}}}{{{ ext{dx}}}} + 6{ ext{y}} = 0$$
Correct Answer
(B) y = e 2x + e 3x
[#13] Solution of $$frac{{{ ext{dy}}}}{{{ ext{dx}}}} = - frac{{ ext{x}}}{{ ext{y}}}$$ xa0 at x = 1 and y = √3 is
Correct Answer
(D) x 2 + y 2 = 4
[#14] The solution to the ordinary differential equation $$frac{{{{ ext{d}}^2}{ ext{y}}}}{{{ ext{d}}{{ ext{x}}^2}}} + frac{{{ ext{dy}}}}{{{ ext{dx}}}} - 6{ ext{y}} = 0$$ xa0 xa0is
Correct Answer
(C) y = c 1 e -3x + c 2 e 2x
[#15] Consider the differential equation $$frac{{{ ext{dy}}}}{{{ ext{dx}}}} = 1 + {{ ext{y}}^2}.$$ Which one of the following can be a particular solution of this differential equation?
Correct Answer
(A) y = tan(x + 3)