83.23.9 problem 9

Internal problem ID [19290]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 01:24:32 PM
CAS classification : [_quadrature]

\begin{align*} y^{2}+{y^{\prime }}^{2}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 29

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

\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= 1 \\ y \left (x \right ) &= -\sin \left (-x +c_{1} \right ) \\ y \left (x \right ) &= \sin \left (-x +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 41

DSolve[y[x]^2+D[y[x],x]^2==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sin (x-c_1) \\ y(x)\to \sin (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}