29.37.21 problem 1143

Internal problem ID [5679]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1143
Date solved : Monday, January 27, 2025 at 01:06:37 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 24

dsolve(ln(diff(y(x),x))+x*diff(y(x),x)+a = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (x \,{\mathrm e}^{-a}\right )^{2}}{2}+\operatorname {LambertW}\left (x \,{\mathrm e}^{-a}\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{2} W\left (e^{-a} x\right )^2+W\left (e^{-a} x\right )+c_1 \]