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Given y'(x) =
√(-4y(x) + 28) and y(-2)=-2, find y(x)?

1 Answer

3 votes
I saw this question the first time around missing those parentheses around the
x, which made the ODE much, much more difficult to solve. This is doable, especially because this ODE is separable.


(\mathrm dy)/(\mathrm dx)=√(-4y+28)

(\mathrm dy)/(2√(7-y))=\mathrm dx

\displaystyle\frac12\int(\mathrm dy)/(√(7-y))=\int\mathrm dx

-√(7-y)=x+C

√(7-y)=-x+C

7-y=(C-x)^2

y=7-(C-x)^2

Given that
y(-2)=-2, we have


-2=7-(C+2)^2

\implies C=-5,C=1

So there are two possible particular solutions:


\begin{cases}y=-x^2-10x-18\\y=-x^2+2x+6\end{cases}
User DamianoPantani
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