Internal problem ID [8014]
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]
Solve \begin {gather*} \boxed {y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 7
dsolve(diff(y(x),x)-1 = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+x \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 125
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 {x \tanh (-\log (x)+c_1)}{\sqrt {\text {sech}^2(-\log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (-\log (x)+c_1)}{\sqrt {\text {sech}^2(-\log (x)+c_1)}} \\ y(x)\to -\frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ y(x)\to \frac {x \tanh (\log (x)+c_1)}{\sqrt {\text {sech}^2(\log (x)+c_1)}} \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}