75.11.9 problem 268

Internal problem ID [16860]
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
Date solved : Tuesday, January 28, 2025 at 09:35:34 AM
CAS classification : [_quadrature]

\begin{align*} \left (y^{\prime }-1\right )^{2}&=y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve((diff(y(x),x)-1)^2=y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= -1+{\mathrm e}^{x} c_{1} \\ y &= 1+c_{1} {\mathrm e}^{-x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 37

DSolve[(D[y[x],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*}