Porisma

A hint to get started

Sketch three upper solution relations and qualify their endpoints

Show the general solution of y dy/dx=2x−1y\,dy/dx=2x-1, y≥0y\ge0, is y2=2x2−2x+Cy^2=2x^2-2x+C. On one diagram sketch the members with C=−1,0,1C=-1,0,1.

CJC · Lecture · Example 13

Integrate first, then use the nonnegative root and check where each radicand is positive.

Read the worked solution