83.2.4 problem 4

Internal problem ID [19050]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 12:48:09 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 51

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

\begin{align*} y \left (x \right ) &= \frac {-c_{1} x -\sqrt {2 x^{2} c_{1}^{2}+1}}{c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} x +\sqrt {2 x^{2} c_{1}^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.436 (sec). Leaf size: 94

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

\begin{align*} y(x)\to -x-\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -x+\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -\sqrt {2} \sqrt {x^2}-x \\ y(x)\to \sqrt {2} \sqrt {x^2}-x \\ \end{align*}