83.23.12 problem 12

Internal problem ID [19293]
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 : 12
Date solved : Tuesday, January 28, 2025 at 01:24:34 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.026 (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: 0.006 (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*}