60.3.298 problem 1304

Internal problem ID [11308]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1304
Date solved : Monday, January 27, 2025 at 11:11:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 38

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

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

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 44

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

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