56.2.49 problem 48

Internal problem ID [8853]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 48
Date solved : Monday, January 27, 2025 at 05:06:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-1/x*diff(y(x),x)-x^2*y(x)-x^3-1/x=0,y(x), singsol=all)
 

\[ y = \sinh \left (\frac {x^{2}}{2}\right ) c_{2} +\cosh \left (\frac {x^{2}}{2}\right ) c_{1} -x \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-1/x*D[y[x],x]-x^2*y[x]-x^3-1/x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh \left (\frac {x^2}{2}\right )+i c_2 \sinh \left (\frac {x^2}{2}\right )-x \]