60.1.378 problem 379

Internal problem ID [10392]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 379
Date solved : Monday, January 27, 2025 at 07:38:54 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 22

dsolve(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}}{4} \\ y &= c_{1} \left (x +1-c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 28

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

\begin{align*} y(x)\to c_1 (x+1-c_1) \\ y(x)\to \frac {1}{4} (x+1)^2 \\ \end{align*}