60.3.398 problem 1404

Internal problem ID [11408]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1404
Date solved : Monday, January 27, 2025 at 11:19:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x^{3}}-\frac {\left (-2 x^{2}+1\right ) y}{4 x^{6}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(diff(y(x),x),x) = -(2*x^2+1)/x^3*diff(y(x),x)-1/4*(-2*x^2+1)/x^6*y(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {1}{4 x^{2}}} \left (c_{1} x +c_{2} \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}] == -1/4*((1 - 2*x^2)*y[x])/x^6 - ((1 + 2*x^2)*D[y[x],x])/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\frac {1}{4 x^2}} (c_2 x+c_1)}{x} \]