Solve the differential equation dy/dx = y^2.

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Question: Solve the differential equation dy/dx = y^2.

Options:

Correct Answer: y = 1/(C - x)

Solution:

This is a separable equation. Integrating gives y = 1/(C - x), where C is the constant.

Solve the differential equation dy/dx = y^2.

Solve the differential equation dy/dx = y^2.

Step 1: Start with the differential equation dy/dx = y^2.
Step 2: Recognize that this is a separable equation, meaning we can separate the variables y and x.
Step 3: Rewrite the equation as dy/y^2 = dx.
Step 4: Integrate both sides. The left side becomes -1/y, and the right side becomes x + C, where C is the constant of integration.
Step 5: After integrating, we have -1/y = x + C.
Step 6: Rearrange the equation to solve for y: y = -1/(x + C).
Step 7: To make it look nicer, we can write it as y = 1/(C - x) by changing the sign.

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