29.37.28 problem 1150

Internal problem ID [5686]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1150
Date solved : Monday, January 27, 2025 at 01:06:57 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime } \ln \left (y^{\prime }\right )-\left (1+x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 18

dsolve(diff(y(x),x)*ln(diff(y(x),x))-(1+x)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.539 (sec). Leaf size: 21

DSolve[D[y[x],x]*Log[D[y[x],x]] -(1+x)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x+1-\log (c_1)) \\ y(x)\to 0 \\ \end{align*}