29.19.15 problem 528

Internal problem ID [5124]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 19
Problem number : 528
Date solved : Monday, January 27, 2025 at 10:13:05 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 22

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

\[ y \left (x \right ) = x \left (2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {1}{2}-\frac {c_{1}}{2}}}{2 \sqrt {x}}\right )+1\right ) \]

✓ Solution by Mathematica

Time used: 6.875 (sec). Leaf size: 35

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

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