MATH/CMSC 206 - Introduction to Matlab

Answers to Self-Test

1. To say that the derivative is 15 percent of the function is to say that it's 0.15 times the original function. Thus:

dsolve('Dy=0.15*y','x')

 
ans =
 
C11*exp((3*x)/20)

2. This is just plug-and-chug:

dsolve('Dy=y+y*sqrt(t)','t')

 
ans =
 
C13*exp(t + (2*t^(3/2))/3)

3. Remember that passing through (0,2) is equivalent to having y(0)=2 and so we solve the initial value problem:

dsolve('Dy-2*y+x=5','y(0)=2','x')

 
ans =
 
x/2 + (17*exp(2*x))/4 - 9/4

4. For this we simply wrap the result of the previous calculation into a subs command:

subs(dsolve('Dy-2*y+x=5','y(0)=2','x'),'x',1)

ans =

   29.6535