Internal problem ID [3834]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1150.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
Solve \begin {gather*} \boxed {y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve(diff(y(x),x)*ln(diff(y(x),x))-(1+x)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = {\mathrm e}^{x} \\ y \relax (x ) = c_{1} x -c_{1} \ln \left (c_{1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.499 (sec). Leaf size: 21
DSolve[y'[x] Log[y'[x]] -(1+x) y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+1-\log (c_1)) \\ y(x)\to 0 \\ \end{align*}