7 results.
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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
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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
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Question in Bill's workspace
Solve for $x$: $a\cosh(x)+b\sinh(x)=c$. There are two solutions for this example.
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Question in Bill's workspace
Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$.
Hence, or otherwise, find roots of $ax^2+bx+c=0$.
Includes a video which shows how to solve a quadratic by completing the square.
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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 $y'(0)=c$.
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Question in Transition to university
Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.
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Question in Transition to university
This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.
