29.6.17 problem 163

Internal problem ID [4763]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 163
Date solved : Monday, January 27, 2025 at 09:36:43 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x y^{\prime }+x^{2}+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x*diff(y(x),x)+x^2+y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left (c_{1} \operatorname {BesselY}\left (1, x\right )+\operatorname {BesselJ}\left (1, x\right )\right ) x}{c_{1} \operatorname {BesselY}\left (0, x\right )+\operatorname {BesselJ}\left (0, x\right )} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 45

DSolve[x D[y[x],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*}