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Separable first order ODE with boundary condition
Solve for $x(t)$, $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
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Second order ODE with constant coefficients and boundary conditions
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$.
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Last modified 17/01/2019 16:16
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Roots of a cubic real polynomial
Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.
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Roll a pair of dice  find probability at least one die shows a given number.
Rolling a pair of dice. Find probability that at least one die shows a given number.
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Solve a second order ODE with repeated roots,
Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$. (Equal roots example).
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Last modified 15/01/2019 19:20
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Solve a pair of simultaneous equations
Solve for $x$ and $y$: \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray} \]
The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
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Last modified 15/01/2019 19:07
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Last modified 15/01/2019 18:48
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