Harry's copy of Solve a second order ODE with repeated roots,

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Harry Flynn

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Harry Flynn 7 years, 1 month ago

Created this as a copy of Solve a second order ODE with repeated roots, .

Name	Status	Author	Last Modified
Solve a second order ODE with repeated roots,	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Harry's copy of Solve a second order ODE with repeated roots,	draft	Harry Flynn	09/03/2018 14:22
Differential Equations: Second Order Repeated Roots	draft	Clare Lundon	08/04/2020 20:04

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Question statement

Find the solution of:

$\simplify[std]{(d^2y/dx^2)+{2*a}*(dy/dx)+{a^2}y}=0$
which satisfies

$y(0)=\var{c}$ and

$y(1)=\var{d}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-5
f1	number	-3.987
c	integer	4
b	integer	4
d	integer	2
f	number	-3.986524106
s	integer	-1

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Name

Data type

Value

xxxxxxxxxx
 
s*random(1..7)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-5

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Mathematical expression
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Gap-fill

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Solution is:

$y=\;\;$ Unnamed gap

Input all numbers correct to 3 decimal places.

Advice

The auxillary equation is $\simplify[std]{lambda^2+{2*a}lambda+{a^2}}=0$ .

On solving this equation we get $\lambda=\var{-a}$ twice.

Hence the general solution is:

$y = \simplify[std]{A*e^({-a}x)+B*x*e^({-a}x)}$
The boundary conditions give:

$y(0)=\var{c} \Rightarrow A=\var{c}$

$y(1)=\var{d} \Rightarrow \simplify{Ae^{-a}+Be^{-a}={d}}\Rightarrow A+B = \simplify{{d}e^{a}}$

So $B=\simplify{{d}e^{a}-{c}}=\var{f1}$ to 3 decimal places.

Hence the solution is:

$y=\simplify{(({c} * Exp(({( - a)} * x))) + ({f1} * x * Exp(({( - a)} * x))))}$

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Harry's copy of Solve a second order ODE with repeated roots,

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Harry Flynn 7 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Harry's copy of Solve a second order ODE with repeated roots,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`