83.20.3 problem 3

Internal problem ID [19241]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (C) at page 56
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:15:24 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 3.666 (sec). Leaf size: 22

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

\[ y(x)\to a \log \left (e^{\frac {x}{a}}+\frac {c_1}{a}\right ) \]