Find the solution of the differential equation dy/dx = y^2.

Find the solution of 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: To solve for y, take the reciprocal of both sides: y = -1/(x + C).
Step 7: To match the short solution format, we can rewrite it as y = 1/(C - x) by adjusting the constant.

Separable Differential Equations – The equation can be separated into functions of y and x, allowing for integration on both sides.
Integration Techniques – Understanding how to integrate functions and apply constants of integration correctly.
General Solution – Recognizing that the solution includes an arbitrary constant (C) which represents a family of solutions.