60.3.439 problem 1446

Internal problem ID [11449]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1446
Date solved : Monday, January 27, 2025 at 11:22:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 31

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

\[ y(x)\to e^{-\frac {1}{x}-\frac {1}{2}} \left (c_1-e c_2 \operatorname {ExpIntegralEi}\left (\frac {2}{x}\right )\right ) \]