If we denote dy/dx by p then the differential equation will be of the form f(x,y,p) = 0
- Solvable for p
If it is solvable for p then solve and integrate the result.
- Equation solvable for y
- Differentiate the given equation w.r.t. x.
- Eliminate p from the given equation and the equation obtained as above.
- The eliminant is the required solution.
- Equation solvable for x
- Differentiate the given equation w.r.t. y.
- Solve the equation obtained for p.
- Eliminate p by putting the value of p in the given equation.
- The eliminant is the required solution.
- Clairaut's equation