29.37.26 problem 1148

Internal problem ID [5684]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1148
Date solved : Monday, January 27, 2025 at 01:06:49 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 38

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 \ln \left ({\mathrm e}^{\frac {-c_{1} +x}{a}}\right )+a \,{\mathrm e}^{\frac {-c_{1} +x}{a}}+x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.373 (sec). Leaf size: 22

DSolve[a*(Log[D[y[x],x]]-D[y[x],x])-x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to a e^{\frac {x-c_1}{a}}+c_1 \]