29.37.22 problem 1144

Internal problem ID [5680]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1144
Date solved : Monday, January 27, 2025 at 01:06:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \ln \left (-\frac {1}{x}\right )+a -1 \\ y \left (x \right ) &= \ln \left (c_{1} \right )+c_{1} x +a \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 27

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

\begin{align*} y(x)\to a+c_1 x+\log (c_1) \\ y(x)\to a+\log \left (-\frac {1}{x}\right )-1 \\ \end{align*}