82.8.2 problem Ex. 2

Internal problem ID [18750]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 25
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:14:24 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 67

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

\begin{align*} y \left (x \right ) &= \sqrt {4 \,\operatorname {Ei}_{1}\left (-\frac {2}{x}\right ) {\mathrm e}^{-\frac {2}{x}}+{\mathrm e}^{-\frac {2}{x}} c_{1} +2 x} \\ y \left (x \right ) &= -\sqrt {4 \,\operatorname {Ei}_{1}\left (-\frac {2}{x}\right ) {\mathrm e}^{-\frac {2}{x}}+{\mathrm e}^{-\frac {2}{x}} c_{1} +2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.029 (sec). Leaf size: 76

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

\begin{align*} y(x)\to -e^{-1/x} \sqrt {-4 \operatorname {ExpIntegralEi}\left (\frac {2}{x}\right )+2 e^{2/x} x+c_1} \\ y(x)\to e^{-1/x} \sqrt {-4 \operatorname {ExpIntegralEi}\left (\frac {2}{x}\right )+2 e^{2/x} x+c_1} \\ \end{align*}