15.21.4 problem 26

Internal problem ID [3328]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 26
Date solved : Monday, January 27, 2025 at 07:34:15 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 25

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

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