Internal problem ID [3116]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 368.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 58
dsolve(x*(c*x^2+b*x+a)*diff(y(x),x)+x^2-(c*x^2+b*x+a)*y(x) = y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (\frac {c_{1} \sqrt {4 a c -b^{2}}+2 \arctan \left (\frac {2 c x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right ) x \]
✓ Solution by Mathematica
Time used: 1.261 (sec). Leaf size: 62
DSolve[x(a+b x +c x^2)y'[x]+x^2-(a+b x+c x^2)y[x]==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \tanh \left (\frac {2 \text {ArcTan}\left (\frac {b+2 c x}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}+c_1\right ) \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}