60.1.397 problem 399

Internal problem ID [10411]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 399
Date solved : Monday, January 27, 2025 at 07:40:41 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 22

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

\begin{align*} y &= -\frac {\left (x -1\right )^{2}}{8} \\ y &= c_{1} \left (2 c_{1} +x -1\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 28

DSolve[-y[x] + (-1 + x)*D[y[x],x] + 2*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x-1+2 c_1) \\ y(x)\to -\frac {1}{8} (x-1)^2 \\ \end{align*}