An Elementary Course in Differential Equations

Cover An Elementary Course in Differential Equations
An Elementary Course in Differential Equations
Edward Joseph Maurus
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30.
sin - = ex 2 . X b) b ce~ x . Sin 2 x siny = c. X siny + x 2 y y cosx = c. X + y + 2 = c(xy + x + i/ 2). Xlogxy -cy. X 3 x 5 ?/ 2 = c.
sin- 1 - = ex 2 . X x = y 2 (x 2 + c). X 3x?/ 2 + x 5 = c.
v log- = c. X 46 DIFFERENTIAL EQUATIONS EXERCISE 10 1. (y- 2. (y - 4x + c) (y + 3x + c) = 0.
3- (y - c) (y - 4x + c) (y + 3x + c) = 0.
4. (y-2x + c)(i/ + x + c)(2y-x + c) = 0.
5. (2/-2x + c)0/-3x + c)(?/-4x + c) = 0.
6. (y - ce-x) (x 2 + 2 T/ + c) = 0.
7. (x 2 - 2 y + c) (x 2 - y + c) (3x 2 - 2 y + c
...) = 0.
8. Y x + c; y l = c(x + l).
9. (y x + c) (xy ex 1) = 0.
10. X 2 + (y - c) 2 = 1.
11. (xy c)(y cx) = 0.
12. (xy - c) (x 2 + y 2 - c) = 0.
EXERCISE 11 2i *Q C O C X o Cy ~r 1.
I / *... . I, 3 p2 ' 7. Y = ex + c 2 ; singular solution, x 2 + 4 ?/ = 0.
p2 2 c 8. Y = ex + tan -1 c ; no singular solution.
3 9. Y = 2. Y = ce 1 + c 2 . Singular solution, x 2 + y 2 = 36.
3. Y = c log x + c 2 . 10. Y = ex + - ; singular solution, y 2 = 4 ox.
4. Y = ex 2 + c 2 . C 5. Ex 8 = (y c) 2 . 11. Y = ex + c Vc 2 + 1.


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