Internal problem ID [3832]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1148.
ODE order: 1.
ODE degree: -1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 45
dsolve(a*(ln(diff(y(x),x))-diff(y(x),x))-x+y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = a +x \\ y \relax (x ) = -a \left (\ln \left ({\mathrm e}^{-\frac {c_{1}}{a}+\frac {x}{a}}\right )-{\mathrm e}^{-\frac {c_{1}}{a}+\frac {x}{a}}\right )+x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.377 (sec). Leaf size: 22
DSolve[a (Log[y'[x]]-y'[x])-x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a e^{\frac {x-c_1}{a}}+c_1 \\ \end{align*}