Internal problem ID [4340]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1148.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )+y=x} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = x +a y \left (x \right ) = -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: 0.355 (sec). Leaf size: 22
DSolve[a (Log[y'[x]]-y'[x])-x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to a e^{\frac {x-c_1}{a}}+c_1 \]