82.21.1 problem Ex. 1

Internal problem ID [18854]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems at page 47
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:30:55 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 35

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

\begin{align*} y \left (x \right ) &= \frac {2 \sqrt {x}\, \left (-x +3 a \right )}{3}+c_{1} \\ y \left (x \right ) &= -\frac {2 \sqrt {x}\, \left (-x +3 a \right )}{3}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 43

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

\begin{align*} y(x)\to -\frac {2}{3} \sqrt {x} (x-3 a)+c_1 \\ y(x)\to \frac {2}{3} \sqrt {x} (x-3 a)+c_1 \\ \end{align*}