Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Find the general solution of $y''+2py'+(p^2-q^2)y=x$ in the form  $Ae^{ax}+Be^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral.

rebelmaths

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

rebelmaths

Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

rearranging the Michelas-Menten equation to make the substrate the subject.

rebelmaths

Rearranging equations by multiplying or dividing: One step

rebelmaths

Simultaneous Equations

rebelmaths

Word Problems leading to simultaneous Linear Equations

rebelmaths

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Shows how to define variables to stop degenerate examples.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Matching a straight line graph to its equation.

Simple Linear Equation.

$ \dfrac{n}{a} \pm b = c$

Solving simple simultaneous equations.

Equations of type ax-b = c.

Includes advice.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

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For Nursing and midwifery

For Nursing and midwifery

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Three items of work done on a car. Given total price, and a couple of ratios of prices between pairs of items, work out the cost of one of the items.

Based on question 4 from section 3 of the Maths-Aid workbook on numerical reasoning.

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

A simultaneous equations question with integers only

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.