class notes and worksheets

Section 1.2 Worksheet MAT–283 Di↵erential Equations


y = 1/ 1 + c e x is a one-parameter family of solutions of the first-order DE y 0 = y y 2 . Find a solution of
the first-order IVP consisting of this di↵erential equation and the given initial condition.
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1 2. y( 1) = 2
1. y(0) =
3

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y = 1/ x + c is a one-parameter family of solutions of the first-order DE y 0 + 2xy 2 = 0. Find a solution of
2

the first-order IVP consisting of this di↵erential equation and the given initial condition. Give the largest
interval I over which the solution is defined.

1 5. y(0) = 1 Thieme
3. y(2) =
3 5 1
1


4. y( 2) =
4 4
1
ii 6. y(1/2) = 4 21 0
2
1
2



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x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x00 + x = 0. Find a
solution of the second-order IVP consisting of this di↵erential equation and the given initial conditions.

7. x(0) = 1; x0 (0) = 8 Tyosco 9. 1
Ea
x0 (⇡/6) = 0
8 cis x(⇡/6) =
2
;
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8. x(⇡/2) = 0; x0 (⇡/2) = 1 10. x(⇡/4) =
p
2;
p
x0 (⇡/4) = 2 2 1 1,63 12

IEEE
y = c1 ex + c2 e x is a two-parameter family of solutions of the second-order DE y 00 y = 0. Find a solution
of the second-order IVP consisting of this di↵erential equation and the given initial conditions.

11. y(0) = 1; y 0 (0) = 2 13. y( 1) = 5; y 0 ( 1) = 5 4 12
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12. y(1) = 0; y 0 (1) = e
E 14. y(0) = 0;
E
y 0 (0) = 0
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