29.30.4 problem 862

Internal problem ID [5444]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 862
Date solved : Monday, January 27, 2025 at 11:24:05 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 49

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 60

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

\begin{align*} y(x)\to c_1 \left (x+\frac {a}{1+c_1}\right ) \\ y(x)\to \left (\sqrt {a}-i \sqrt {x}\right )^2 \\ y(x)\to \left (\sqrt {a}+i \sqrt {x}\right )^2 \\ \end{align*}