University:
Whitman College
Course:
MATH-244 | Differential Equations
Academic year:

2023
Views:

70

Pages:

1
Author:

Edwin Conner

Solutions to Practice Problems: 1. C1 + C2 = 2 −2C1 − 3C2 = 3 Solution: C1 = 2. 2 1 3 −3 1 1 −2 −3 = −9 −6 − 3 = =9 −3 + 2 −1 C2 = 1 2 −2 3 −1 = 3+4 = −7 −1 C1 + C2 = y0 r1 C1 + r2 C2 = v0 Solution: y0 1 v 0 r2 C1 = 1 1 r1 r2 = y 0 r2 − v 0 r2 − r1 1 y0 r1 v 0 v 0 − r1 y 1 C2 = = r2 − r1 r2 − r1 NOTE: A unique solution to the system of equations exists iff r1 6= r2 . 3. C1 + C2 = 2 3C1 + C2 = 1 Solution: C1 = 2 1 1 1 1 1 3 1 = 1 1 =− −2 2 C2 = 1 2 3 1 −2 = −5 5 = −2 2 4. 2C1 − 5C2 = 3 . No solution to this array (think of it as two parallel lines). 6C1 − 15C2 = 10 5. 2x − 3y = −1 3x − 2y = 1 Solution: x= −1 −3 1 −2 2 −3 3 −2 = 2+3 =1 −4 + 9 y= 2 −1 3 1 5 = 2+3 =1 5

Math 244 Solutions to Practice Problems - Answer Key

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