60.1.423 problem 425

Internal problem ID [10437]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 425
Date solved : Monday, January 27, 2025 at 07:43:50 PM
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: 0.077 (sec). Leaf size: 45

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 51

DSolve[y[x] - (x + y[x])*D[y[x],x] + (1 + x)*D[y[x],x]^2==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*}