75.11.4 problem 263

Internal problem ID [16855]
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 : 263
Date solved : Tuesday, January 28, 2025 at 09:35:14 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x)^2-y(x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 28

DSolve[D[y[x],x]^2-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to c_1 e^x \\ y(x)\to 0 \\ \end{align*}