83.18.10 problem 10

Internal problem ID [19220]
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 (A) at page 53
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:14:04 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)^2+(y(x)-x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

DSolve[x*D[y[x],x]^2+(y[x]-x)*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x} \\ y(x)\to x+c_1 \\ y(x)\to 0 \\ \end{align*}