Math 415.01 - Dr. Huseyin Coskun - Solutions to HW 2
- 10:30 recitation (Vutha)
January 19, 2011
The homework will be graded for 25 pts. (Completion: 5 pts , Graded questions: 20 pts)
(2.2.19) The given equation
sin(2x)dx + cos(3y )dy = 0
) A car increases its speed at a constant rate from 40 mi/h at A to 60 mi/h at B. What is the
magnitude of its acceleration 2 s after the car passes point A?
02Di = -6 2 ,g3
Verify that y1 (t) = t/4 and y2 (t) = et + t/4 are solutions to y
+ 5 y + 4 y = t.
We rst take derivatives: y1 (t) = 1/4 so y1 (t) = 0 = y1 (t) = y1 (t). Also, y2 (t) = et + 1/4, y2 (t) = et ,
y2 (t) = et , and y2 (t) = et . So
Math 415.01 - Dr. Huseyin Coskun - Quiz 1 - 10:30
January 12, 2011
(1) Solve the given set of equations, or else show that there is no solution.
x1 + x2 + x3 = 6
2x1 + x2 + x3 = 0
x1 + 2 x2 x3 = 1
(2) For the given dierent
Find the solution of
3 x2 + ex
y (0) = 1,
and determine (approximately) where the solution is dened.
The equation separates as (2y 10)dy = (3x2 + ex )dx and so has implicit solution y 2 10y = x3 + ex + C .
Using the initi
For the dierential equation y = y 2 (1 y 2 ), sketch the graph of f (y ) versus y , determine the equilibrium
points, and classify them. Draw the phase line and several solutions for < y0 < (where y (0) = y0 ).
Determine (without solving) an interval in which the solution of
(t 4)y + (ln t)y = 2t,
y (1) = 3
is certain to exist.
Writing this linear equation in standard form we have
The function t/(t 4) is discontinuous