Differential Equations/Separable 3

Current revision (unreviewed)

[edit] Existence problems

Tell whether the following initial value problems have a solution or not, and if its solution is unique.

1) $y' = (12 x 2 + 5 x)(y + 9 y 3), y (7) = 11$

2) $y' = l n (7 x), y ( - 1) = 10$

3) $y'=\frac{x+7x^2-6x^3}{y^2-1},y(0)=16$

4) $y' = x l n (y - 1), y (1) = 1$

5) $y'=\frac{x^3+5x}{y^2+7y+12},y(5)=9$

6) $y'=\frac{y+7y^2}{x-5},y(5)=4$

7) $y' = y 3 s e c 2 (x),$

8) $y'=\frac{5y^2+6}{y}$

9) $y' = x 3 / y 3$

10) $y' = x 2 + 3 x - 9$

11) $y' = c o s (y) / s i n (y)$

12) $y'=\frac{cos(x)}{sin(y)}$

13) $y' = c o s (x) + s i n (x), y (0) = 1$

14) $y' = 7 y 2, y (5) = 9$