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Үндсэн товъёог

Course: AP®︎ Calculus AB > Unit 7

Lesson 5: Finding general solutions using separation of variables

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Separable differential equations: find the error

Гүүгэл анги

Kajal tried to solve the differential equation

\frac{d y}{d x} = - x^{2} y^{2}

. This is her work:

\begin{aligned} \frac{d y}{d x} & = - x^{2} y^{2} \\ Step 1: & \int - y^{- 2} d y & = \int x^{2} d x \\ Step 2: & y^{- 1} & = \frac{x^{3}}{3} + C \\ Step 3: & y & = \frac{3}{x^{3}} + C \end{aligned}

Is Kajal's work correct? If not, what is her mistake?

(Сонголт A)
Kajal's work is correct.
(Сонголт B)
Step 1 is incorrect. The separation of variables wasn't done correctly.
(Сонголт C)
Step 2 is incorrect. Kajal didn't integrate $x^{2}$ ‍ correctly.
(Сонголт D)
Step 3 is incorrect. Kajal didn't take the reciprocal of $\frac{x^{3}}{3} + C$ ‍ correctly.