60.3.195 problem 1199

Internal problem ID [11205]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1199
Date solved : Monday, January 27, 2025 at 10:48:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

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

\[ y = x \left (\operatorname {Ei}_{1}\left (x \right ) {\mathrm e}^{x} c_{2} x^{3}+{\mathrm e}^{x} x^{3} c_{1} -c_{2} \left (x^{2}-x +2\right )\right ) \]

✓ Solution by Mathematica

Time used: 60.025 (sec). Leaf size: 39

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

\[ y(x)\to e^{x+4} x^4 \left (\int _1^x\frac {e^{-K[1]-4} c_1}{K[1]^4}dK[1]+c_2\right ) \]