Page 88 - MATLAB an introduction with applications

MATLAB Basics ——— 73

(c) >> S3=sqrt (x)
>> int (S3)
ans =
2/3*x^ (3/2)
>> int (S3,‘a’, ‘b’)
ans =
2/3*b^ (3/2)–2/3*a^ (3/2)
>> int (S3, 0.4, 0.7)
ans =
7/150*70^ (1/2)–4/75*10^ (1/2)

(d) >> S4 = 7*x^5–6*x^4+11*x^3+4*x^2+8*x–9
>> int (S4)
ans =
7/6*x^6–6/5*x^5+11/4*x^4+4/3*x^3+4*x^2–9*x
(e) >> S5=cos (a)
>> int (S5)
ans =
sin (a)

Example E1.24: Obtain the general solution of the following first order differential equations:
2
dy dy dy
t
(a) = 5 − y (b) 2 + 3 + y = 0
6
dt dt dt
ds ds
(c) = Ax 3 (d) = Ax 3
dt dA
Solution:
(a) >> solve (‘Dy=5*t–6*y’)
ans =
5/6*t–5/36+exp (–6*t)*C1
(b) >> dsolve (‘D2y +3*Dy + y = 0’)
ans =
C1*exp (1/2*(5^ (1/2)–3)*t) + C2*exp (–1/2*(5^ (1/2) +3)*t)
(c) >> dsolve (‘Ds =A*x^3’,‘x’)
ans =
1/4*A*x^4 + C1
(d) >> dsolve (‘Ds=A*x^3’, ‘A’)
ans =
1/2*A^2*x^3 + C1

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