60.1.95 problem 95

Internal problem ID [10109]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 95
Date solved : Monday, January 27, 2025 at 06:27:49 PM
CAS classification : [_rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 45

DSolve[x*D[y[x],x] + y[x]^2 + 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*}