75.11.2 problem 261

Internal problem ID [16853]
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 : 261
Date solved : Tuesday, January 28, 2025 at 09:35:06 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.078 (sec). Leaf size: 15

dsolve(diff(y(x),x)^2-4*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \left (x -c_{1} \right )^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 38

DSolve[D[y[x],x]^2-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} (-2 x+c_1){}^2 \\ y(x)\to \frac {1}{4} (2 x+c_1){}^2 \\ y(x)\to 0 \\ \end{align*}