Internal problem ID [8770]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 434.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 7
dsolve(diff(y(x),x)-1 = 0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +x \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 71
DSolve[-x^2 - 2*x*y[x]*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-c_1} \left (-x^2+e^{2 c_1}\right ) y(x)\to \frac {1}{2} e^{-c_1} \left (-1+e^{2 c_1} x^2\right ) y(x)\to -i x y(x)\to i x \end{align*}