60.3.306 problem 1312

Internal problem ID [11316]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1312
Date solved : Monday, January 27, 2025 at 11:11:14 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x*(x^2+1)*diff(diff(y(x),x),x)+2*(x^2-1)*diff(y(x),x)-2*x*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{3}+c_{1}}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 53

DSolve[-2*x*y[x] + 2*(-1 + x^2)*D[y[x],x] + x*(1 + x^2)*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (c_2 x^3+3 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\frac {2 \left (K[1]^2-1\right )}{K[1]^3+K[1]}dK[1]\right )}{3 x} \]