Download 1. Fill in the blank: by the product rule, (C<) = 2. If y is a function of

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1. Fill in the blank: by the product rule, (♥♦)0 = . . .
2. If y is a function of x, then (yx2 )0 = . . .
3. Consider the DE: y 0 x2 + 2xy = x2
(a) Use #2 to re-write the left-hand side.
(b) Take the anti-derivative of both sides (don’t forget C).
(c) Solve for y.
(d) Check!
4. Compute (yex )0
5. Solve the differential equation: y 0 ex + ex y = sin(x)
6. Solve the differential equation: y 0 sin(x) + y cos(x) = 1
7. Consider the differential equation: y 0 − 2y = 1
(a) Can you solve it?
(b) Multiply both sides by e−2x
(c) Now can you solve it?
8. Consider the differential equation: y 0 + y = e−2x
(a) Can you solve it?
(b) Multiply both sides by ex
(c) Now can you solve it?
9. Consider the differential equation: y 0 + x1 y =
cos(x)
x
(a) Can you solve it?
(b) Multiply both sides by x
(c) Now can you solve it? Yes! Do it!
10. Consider the differential equation: y 0 + 2xy = x
(a) Can you solve it?
(b) Multiply both sides by ex
2
(c) Now can you solve it? Yes! Do it!
11. Solve the DE: y 0 + 3y = 2 (HINT: multiply both sides by e3x )
12. Solve the DE: y 0 + 3y = e5x
13. Solve the DE: y 0 + 3y = x
14. Solve the DE: y 0 + 4y = 1
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