Equation of first order and higher degree

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
    1. Differentiate the given equation w.r.t. x.
    2. Eliminate p from the given equation and the equation obtained as above.
    3. The eliminant is the required solution.
  • Equation solvable for x
    1. Differentiate the given equation w.r.t. y.
    2. Solve the equation obtained for p.
    3. Eliminate p by putting the value of p in the given equation.
    4. The eliminant is the required solution.
  • Clairaut's equation



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