60.3.339 problem 1345

Internal problem ID [11349]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1345
Date solved : Monday, January 27, 2025 at 11:17:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {y^{\prime }}{x^{3}}+\frac {2 y}{x^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 45

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

\[ y(x)\to \frac {1}{2} e^{\frac {1}{2 x^2}} x \left (2 c_1-\sqrt {2 \pi } c_2 \text {erf}\left (\frac {1}{\sqrt {2} x}\right )\right ) \]