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Performing the integration by hand, we can only get it as far as:
because the integral of exp(x)/x is not available in closed form.
Example 3
– Solving an equation with initial conditions. Solve
d
2
y/dt
2
+ 5y = 2 cos(t/2),
with initial conditions
y(0) = 1.2, y’(0) = -0.5.
In the calculator, use:
[‘d1d1y(t)+5*y(t) = 2*COS(t/2)’ ‘y(0) = 6/5’ ‘d1y(0) = -1/2’] `
‘y(t)’ `
DESOLVE
Notice that the initial conditions were changed to their
Exact expressions, ‘y(0)
= 6/5’, rather than ‘y(0)=1.2’, and ‘d1y(0) = -1/2’, rather than, ‘d1y(0) = -0.5’.
Changing to these Exact expressions facilitates the solution.
The solution is:
Press μμto simplify the result to
‘y(t) = -((19*√5*SIN(√5*t)-(148*COS(√5*t)+80*COS(t/2)))/190)’.
Note: To obtain fractional expressions for decimal values use function Q
(See Chapter 5).
0
)( Cdx
x
Ce
xy
x
+
+
⋅=
∫
0
ln)( CxCdx
x
e
xy
x
+⋅+⋅=
∫
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