(dy/dx)^2
| Input interpretation |
|---|
| ((dy(x))/(dx))^2 |
| ODE classification |
| first-order nonlinear ordinary differential equation |
| Differential equation solution |
| y(x) = c_1 |
| Series expansion at x=0 |
| y'(0)^2 + 2 x y'(0) y”(0) + x^2 (y”(0)^2 + y^(3)(0) y'(0)) + x^3 (1/3 y^(4)(0) y'(0) + y^(3)(0) y”(0)) + 1/12 x^4 (3 y^(3)(0)^2 + y^(5)(0) y'(0) + 4 y^(4)(0) y”(0)) + O(x^5) (Taylor series) |
| Derivative |
| d/dx(y'(x)^2) = 2 y'(x) y”(x) |