29.37.27 problem 1149

Internal problem ID [5685]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1149
Date solved : Monday, January 27, 2025 at 01:06:53 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.272 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 24

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

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