Ordinary Differential Equations/Separable 3

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Existence problems[edit]

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

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

2) y'=ln(7x),y(-1)=10

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

4) y'=xln(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

Separable equations[edit]

7) y'=y^3sec^2(x),

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

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

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

11) y'=cos(y)/sin(y)

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

Initial value problems[edit]

13) y'=cos(x)+sin(x),y(0)=1

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