Internal problem ID [7676]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 95.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+y^{2}+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 40
dsolve(x*diff(y(x),x) + y(x)^2 + x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {c_{1} x \BesselY \left (1, x\right )}{c_{1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )}-\frac {\BesselJ \left (1, x\right ) x}{c_{1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )} \]
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 45
DSolve[x*y'[x] + y[x]^2 + x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x (Y_1(x)+c_1 J_1(x))}{Y_0(x)+c_1 J_0(x)} \\ y(x)\to -\frac {x J_1(x)}{J_0(x)} \\ \end{align*}