Internal problem ID [8516]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 180.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Riccati]
\[ \boxed {\left (a \,x^{2}+x b +c \right ) \left (y^{\prime } x -y\right )-y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 58
dsolve((a*x^2+b*x+c)*(x*diff(y(x),x)-y(x)) - y(x)^2 + x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = -\tanh \left (\frac {c_{1} \sqrt {4 a c -b^{2}}+2 \arctan \left (\frac {2 a x +b}{\sqrt {4 a c -b^{2}}}\right )}{\sqrt {4 a c -b^{2}}}\right ) x \]
✓ Solution by Mathematica
Time used: 1.181 (sec). Leaf size: 116
DSolve[(a*x^2+b*x+c)*(x*y'[x]-y[x]) - y[x]^2 + x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \left (-1+\exp \left (\frac {4 \arctan \left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}+2 c_1\right )\right )}{1+\exp \left (\frac {4 \arctan \left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {4 a c-b^2}}+2 c_1\right )} y(x)\to -x y(x)\to x \end{align*}