User Guide –

Differential Equations Made Easy

Topic

Description

Correct

Incorrect

1) General usage

a) Multiplication of variables

x*y^2, x*cos(x)

xy^2, xcos(x)

b) Enter .5 instead of ½ to obtain decimal answers.

use ½*x or .5*x

c) Roots: i.e. ³√x

x^(1/3)

3√x

d) Denominators

1/(x-2)

1/x-2

e) Squaring sin(x)

sin(x)^2 or (sin(5x))^2

sin(x^2)

sin^2(5x)

f) Parentheses:

ln(sin(5x))/(x^2-1)
(x^2-9)/(3+x^2)

lnsin(5x)/x^2-1
(x^2-9)/3+x^2

g) Euler Number

e (using Diamond e^x)

e (Alpha e)

2) General usage of DEQME

a) Use ESC to exit the current module or DEQME altogether.

b) Incorrect Entries – see above - yield the error message: “Invalid Entry”. Press ENTER and correct expression.

c) To force decimal answers, use decimal input (see also 1b)

d) Provide 60,000 of Flash ROM (to check:2^nd 6). Deleting or archiving files may be necessary: use 2^nd “–“ (VAR-LINK), F4 to select files, then F1 to delete or archive. Archiving might be a good way to manage programs, variables, etc as a loss of battery power may delete any unarchived files.

e) Emptying the MAIN folder when starting DEQME will prevent any file reoccurrences (and thus loading error).

f) Should Differential Equations Made Easy not start (anymore) or act strange, reset ALL memory (2^nd 6, then F1) as memory may be corrupted.

g) Use the latest Operating System (OS) using TI Connect.

3) Garbage Collection	Nothing to worry about. The calculator reorganizes memory for proper functioning of APPS such as DEQME.
4) Incorrect Program Termination.	If CME is not properly terminated using ESC, these two error messages may occur. Simply press ESC (up to 50 times) , then restart DEQME. If trouble persists: take out all 5 batteries and reinstall DEQME.

5) Any 1. order Differential Equations

Correct:

1) DE=x*y
2) DE=x^3

Incorrect:

1) DE=xy
2) DE=a*x^3

6) Exact Differential Equation

Correct:

M(x,y)=2x^3*y^2

Incorrect:

1) M(x,y)=2xy^2
2) M(x,y)=2*t*y^2

7) Linear in x

Correct:

1) P(y)=y^3
2) Q(y)=y^4

Incorrect:

1) P(y)=x^3
2) P(y)=t^4

8) 1. Order Checker Differential Equations

Correct:

1) DE:: y’=y
2) Solution y=e^(x)

Incorrect:

1) DE:: y’=xy
2) Solution y=e^(t)

9) Bernoulli Differential Equations

Correct:

1) p(x)=x^3
2) n=5

Incorrect:

1) p(x)=y
2) n=a

10) 2. Order Differential Equation

Correct:

1) DE: y’’=x*y

Ind Var=x
Dep Var=y

2) DE: y’’=t^2

Ind Var=t
Dep Var=y

Incorrect:

1) DE: y”=xy
2) DE: y”=a*x^3

11) 2. Order Homogeneous Differential Equation

Correct:

1) b=-3
2) c=2

Incorrect:

1) b=x
2) c=t

12) 2. Order Non-Homogeneous Differential Equation

Correct:

1) b=-3
2) c=2

3) g(x)=x^3

Incorrect:

1) b=x
2) c=t

3) g(x)=t^4

13) 2. Order Differential Equation Solution Checker.

Correct:

1) DE:: y”=4*y
2) DE:: y”=x*y

Incorrect:

1) DE:: y”=xy
2) DE:: y”=t*x^3

Note: Use Single Quote (‘) twice, do not use quotation marks (“).

14) Variation of Parameter for 2. Order DE.

Correct:

1) DE(x,y):
y”-2y’+y=x*y

Incorrect:

1) DE(x,y):
y”-2y’+t=x*y
2) DE(x,y):
4y”-2y’+y=x*y

15) Reduction of Order for 2. Order DE.

Correct:

1) q(x)=1/(2x)
2) y1(x)=cos(√(x))

Incorrect:

1) q(x)=1/t
2) y1(x)=cos(√(y))

16) Legendre Differential Equation

Correct:

1) q(x)=
(-2x)/(1-x^2)

Incorrect:

1) q(x)=1/t

17) Solve a DE of Order n with constant coefficients by entering its corresponding Characteristic Equation in terms of t.

Correct:

1) CharEq(t):
t^3+3t^2-t-3=0

Incorrect:

1) CharEq(t):
x^3+3x^2-x-3=0

18) Solve X’ = A * X

Correct:

1) A= [2,-3;1,-2]
t0 = 0

X(t0)=[1;2]

Incorrect:

1) A=(1,2,3,4)

2) A=(1,2,3;4)

3) X(t0)=[1,2]

19) Solve a DE using LaPlace Transform (step by step)

Correct:

1) DEQ:: y2+4y=sin(2t)

Incorrect:

1) DEQ:: y2+y=sin(t)
2) [y0, y’0, ..] = [0;0]

20) LaPlace Transform

Correct:

1) f(t)=t^2

Incorrect:

1) f(t)=x^2
2) f(s)=s^2

21) Inverse LaPlace Transform

Correct:

1) f(s)=s^2

Incorrect:

1) f(s)=t^2
2) f(s)=x^2

22) Compute Wronskian

Correct:

1) Functions(x)=
[e^(x), e^(2x)]

Incorrect:

1) Functions(x)=
(e^(x), e^(2x))

2) Functions(x)=
[e^(t), e^(2t)]

3) Functions(x)=
[e^(x); e^(2x)]

23) Annihilator Method

Correct:

1) P(d)=d^2-1
2) f(x)=x^3-8

Incorrect:

1) P(d)=d2-1
2) P(d)=x^2-1
3) f(x)=t^3-8

4) f(x)=x3-8

24) Picard Method

Correct:

1) dy/dx=x*y
2) dy/dx=x^3

Incorrect:

1) dy/dx=xy
2) dy/dx=t*y

25) LaPlace Equation

Nothing to enter for this and for the other PDE’s = Partial Differential Equations. Their solutions are simply displayed here.