xy' - ( 1 + x ) y = xy^2
Follow the Step by step (Bernaulli DE):
1. Write the equation into the Bernoulli?s form.
2. Identify P, Q, and n.
3. Let v = y1-n
4. Solve for integrating factor ?
?? = ??(1-n)?P(x)dx or ??=e(1-n)?P(y)dy
5. Multiply both sides of equation by ?.
Note: The integral of the left side is always equal to v?.
General Solution: ???? = (?? ? ??) ? ??(??) ? ?? ???? +??
6. Integrate both sides of equation to get the General Solution.
7. Substitute v = y1-n to have the GS in terms of x and y.