Internal problem ID [3882]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 634.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (x^{2}+y x +a y^{2}\right ) y^{\prime }-y x -y^{2}=x^{2} a} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 105
dsolve((x^2+x*y(x)+a*y(x)^2)*diff(y(x),x) = a*x^2+x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = x^{\frac {-2 a +2}{2+a}} {\mathrm e}^{\frac {\left (-a +1\right ) \operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}}-x^{-\frac {6 a}{2+a}} {\mathrm e}^{-\frac {2 \left (a \textit {\_Z} +3 c_{1} a -\textit {\_Z} \right )}{2+a}}-3 x^{-\frac {3 a}{2+a}} {\mathrm e}^{-\frac {a \textit {\_Z} +3 c_{1} a -\textit {\_Z}}{2+a}}-3\right )-3 c_{1} a}{2+a}}+x \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 54
DSolve[(x^2+x y[x]+a y[x]^2)y'[x]==a x^2+x y[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{3} (a-1) \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\frac {1}{3} (a+2) \log \left (1-\frac {y(x)}{x}\right )=-a \log (x)+c_1,y(x)\right ] \]