## Related questions with answers

Question

Sketch the solutions of the differential equations in Exercise given below. In each case, also indicate the constant solutions.

$y^{\prime}=y^2+y, y(0)=-\frac{1}{3}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 5Consider the differential equation

$y'=g(y)$

where $g(y)=y^2+y=y(y+1)$.

Note that for the zeros of $g(y)$ we have:

$y(y+1)=0 \implies y=0 \quad \lor \quad y=-1$

Then, the differential equation $y'=g(y)$ has the constant solutions $y=0$ and $y=-1$.

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