% --- begin quiz --- % --- quiz heading: SOlution of differential equation % --- previous heading type: exercise % --- keywords: [u'derivatives', u'exponential function', u'equation, differential', u'differential equation'] % --- begin quiz question --- Given \[ \frac{dy}{dx} = -y(x),\quad y(0)=1 \] What is the solution of this equation? % --- end quiz question --- % --- label: quiz:diff:eq1 % --- begin quiz choice 1 (right) --- $y=e^{-y}$ % --- end quiz choice 1 (right) --- % --- begin quiz choice 2 (wrong) --- $y=e^{y}$ % --- end quiz choice 2 (wrong) --- % --- begin explanation of choice 2 --- Almost, but the sign is wrong (note the minus!). % --- end explanation of choice 2 --- % --- begin quiz choice 3 (wrong) --- \bpycod from math import exp def f(x): return exp(x) \epycod % --- end quiz choice 3 (wrong) --- % --- begin explanation of choice 3 --- Ooops, forgot a minus: \texttt{exp(-x)}, otherwise this Python code must be considered as a good answer. It is more natural, though, to write the solution to the problem in mathematical notation: \[ y(x) = e^{-y}.\] % --- end explanation of choice 3 --- % --- begin quiz choice 4 (wrong) --- The solution cannot be found because there is a derivative in the equation. % --- end quiz choice 4 (wrong) --- % --- begin explanation of choice 4 --- Equations with derivatives can be solved; they are termed \emph{differential equations}. % --- end explanation of choice 4 --- % --- begin quiz choice 5 (wrong) --- The equation is meaningless: an equation must be an equation for $x$ or $y$, not a function $y(x)$. % --- end quiz choice 5 (wrong) --- % --- begin explanation of choice 5 --- Equations where the unknown is a function, as $y(x)$ here, are called \emph{differential equations}, and are solved by special techniques. % --- end explanation of choice 5 --- % --- end quiz --- % --- begin quiz --- % --- new quiz page: Test of quizzes % --- quiz heading: Capital of Norway % --- previous heading type: subsection % --- keywords: [u'capitals', u'basic intelligence', u'geography'] % --- begin quiz question --- [Fundamental test:] What is the capital of Norway? % --- end quiz question --- % --- begin quiz choice 1 (wrong) --- [Answer 1:] Stockholm % --- end quiz choice 1 (wrong) --- % --- begin explanation of choice 1 --- Stockholm is the capital of Sweden. % --- end explanation of choice 1 --- % --- begin quiz choice 2 (wrong) --- [Answer 2:] London % --- end quiz choice 2 (wrong) --- % --- begin quiz choice 3 (right) --- [Answer 3:] Oslo % --- end quiz choice 3 (right) --- % --- begin quiz choice 4 (wrong) --- Bergen % --- end quiz choice 4 (wrong) --- % --- begin explanation of choice 4 --- Those from Bergen would claim so, but nobody else. % --- end explanation of choice 4 --- % --- end quiz ---