Exercise · ZW-SOLUTION-OF-A-DIFFERENTIAL-EQUATION-009 · ★★★ Advanced
The function \(y=\frac{1}{1-x}\) satisfies \(y'=y^2\). On which interval is it a solution?
Choose one option.
Show answer
- C. \((-1,1)\)
Explanation
It is undefined at \(x=1\), so the interval cannot contain it. Only \((-1,1)\) avoids it; the others include \(x=1\).
Review the concept: Solution of a differential equation
A solution \(\varphi\) of a differential equation \(F=0\) is a function that, substituted together with its derivatives, makes the equation a true identity on a whole interval.
\[F\big(x,\varphi(x),\varphi'(x),\dots,\varphi^{(n)}(x)\big)=0\]
More practice problems: solution of a differential equation
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