29.30.18 problem 877

Internal problem ID [5458]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 877
Date solved : Monday, January 27, 2025 at 11:24:39 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.091 (sec). Leaf size: 45

dsolve((1+x)*diff(y(x),x)^2-(x+y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 51

DSolve[(1+x) (D[y[x],x])^2-(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 {c_1}{-1+c_1}\right ) \\ y(x)\to x-2 \sqrt {x+1}+2 \\ y(x)\to x+2 \sqrt {x+1}+2 \\ \end{align*}