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19 results.

Numbas demo: Motion under gravity
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Question in Demos by Christian Lawson-Perfect

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$ . Find time to maximum height and the maximum height. Now includes an interactive plot.
Transfer function from differential equation
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Question in IE303412 Cybernetics by Aleksander Skrede and 1 other

This question tests the students skill on transfer functions and Laplace of differential equations. The coefficients of the functions are created randomly.
Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
Julie's copy of Second order differential equations 2
Draft
Question in Julie's workspace by Julie Crowley

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example). Includes an interactive plot.

rebelmaths
First order differential equations 8
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Question in Bill's workspace by Bill Foster

Solve for $x(t)$ , $\displaystyle\frac{dx}{dt}=\frac{a}{(x+b)^n},\;x(0)=0$
Dynamical system 9: Saddle.
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Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a saddle. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Dynamical system 4
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Question in Bill's workspace by Bill Foster

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.
Dynamical system 7: Stable spiral.
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Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a stable spiral. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Dynamical system 6:Centre.
Draft
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Bill's copy of Dynamical system 6:Centre.
Ready to use
Question in Bill's workspace by Bill Foster

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$
Second order ODE with constant coefficients and boundary conditions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .
Solve a second order ODE with repeated roots,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example).
Solution curves and Vector fields 1 : dy/dx=sin(x-y)
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Question in Bill's workspace by Bill Foster

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$ , 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 $f(x,y)$ .
Solution curves and Vector fields 2 : $dy/dx=x^2-y^2$
Ready to use
Question in Bill's workspace by Bill Foster

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 $f(x,y)$ .
Julie's copy of Second order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

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
Julie's copy of First order differential equations 5
Draft
Question in Julie's workspace by Julie Crowley

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

rebelmaths
Julie's copy of First order differential equations 4
Draft
Question in Julie's workspace by Julie Crowley

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

rebelmaths
Julie's copy of First order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

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
Second order differential equations - sine forcing
Ready to use
Question in Daniel's workspace by Daniel Nucinkis

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$ .

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