Internal problem ID [3419]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 163.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x y^{\prime }+y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(x*diff(y(x),x)+x^2+y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {c_{1} x \operatorname {BesselY}\left (1, x\right )}{c_{1} \operatorname {BesselY}\left (0, x\right )+\operatorname {BesselJ}\left (0, x\right )}-\frac {\operatorname {BesselJ}\left (1, x\right ) x}{c_{1} \operatorname {BesselY}\left (0, x\right )+\operatorname {BesselJ}\left (0, x\right )} \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 45
DSolve[x y'[x]+x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x (\operatorname {BesselY}(1,x)+c_1 \operatorname {BesselJ}(1,x))}{\operatorname {BesselY}(0,x)+c_1 \operatorname {BesselJ}(0,x)} y(x)\to -\frac {x \operatorname {BesselJ}(1,x)}{\operatorname {BesselJ}(0,x)} \end{align*}