Internal problem ID [3359]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 619.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x +y\right )^{2} y^{\prime }-x^{2}+2 y x -5 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve((x+y(x))^2*diff(y(x),x) = x^2-2*x*y(x)+5*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{2 \textit {\_Z}} \ln \relax (x )+{\mathrm e}^{2 \textit {\_Z}} c_{1}+{\mathrm e}^{2 \textit {\_Z}} \textit {\_Z} -4 \,{\mathrm e}^{\textit {\_Z}}-2\right )} x +x \]
✓ Solution by Mathematica
Time used: 0.331 (sec). Leaf size: 41
DSolve[(x+y[x])^2 y'[x]==x^2-2 x y[x]+5 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2-\frac {4 y(x)}{x}}{\left (\frac {y(x)}{x}-1\right )^2}+\log \left (\frac {y(x)}{x}-1\right )=-\log (x)+c_1,y(x)\right ] \]