60.3.277 problem 1282

Internal problem ID [11287]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1282
Date solved : Monday, January 27, 2025 at 11:05:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(x^2+6)*(x^2-4)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{4}} \left (c_{2} x^{5}+c_{1} \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 32

DSolve[(-4 + x^2)*(6 + x^2)*y[x] + 4*x^3*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-\frac {x^2}{4}} \left (c_2 x^5+5 c_1\right )}{5 x^2} \]