MA 238-02: TEST 3 (4/17/09)
1. Use the Laplace transform to solve the initial value problem
y00
−2y0
−3y= 0, y(0) = 2, y0(0) = −3.
2. Use the Laplace transform to solve the initial value problem
y00 + 4y0+ 3y= 3, y(0) = 0, y0(0) = 0.
3. Find L−1·s
s2+ 2s+ 5¸.
4. (a) Use the Laplace transform and the convolution identity to find a formula for
the solution of the initial value problem
y00 +y0
−6y=f(t), y(0) = 0, y0(0) = 0.
(b) Let f(t) = e2tsin 5tin (a). Find y(t).
(Hint: Zeat sin bt dt =eat
a2+b2(asin bt −bcos bt) + c.)
5. (Bouns) (i) Find
L[tsin(kt)].
(ii) Use (i) to find
L−1·s
(s2+ 25)2¸.