83.3.13 problem 13

Internal problem ID [19069]
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 (B) at page 9
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 12:51:12 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 35

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

\[ y \left (x \right ) = x \,{\mathrm e}^{\frac {\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {-c_{1} x +1}{x}}}{x}\right ) x +c_{1} x -1}{x}} \]

✓ Solution by Mathematica

Time used: 5.123 (sec). Leaf size: 30

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

\begin{align*} y(x)\to -\frac {1}{W\left (-\frac {e^{\frac {1}{x}-c_1}}{x}\right )} \\ y(x)\to 0 \\ \end{align*}