Internal problem ID [15130]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 268.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (y^{\prime }-1\right )^{2}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((diff(y(x),x)-1)^2=y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -1+{\mathrm e}^{x} c_{1} \\ y \left (x \right ) &= 1+c_{1} {\mathrm e}^{-x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 37
DSolve[(y'[x]-1)^2==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 e^{-x} \\ y(x)\to -1+c_1 e^x \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}