15.19.12 problem 12

Internal problem ID [3296]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:31:39 AM
CAS classification : [_separable]

\begin{align*} y&=x +3 \ln \left (y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 29

dsolve(y(x)=x+3*ln(diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= x \\ y \left (x \right ) &= x +3 \ln \left (\frac {{\mathrm e}^{-\frac {x}{3}} c_{1}}{-1+c_{1} {\mathrm e}^{-\frac {x}{3}}}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 22

DSolve[y[x]==x+3*Log[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -3 \log \left (e^{-x/3}-\frac {c_1}{3}\right ) \]