81.1.7 problem 6

Internal problem ID [18602]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:03:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+2 y^{\prime }&=y x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)=x*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 28

DSolve[x*D[y[x],{x,2}]+2*D[y[x],x]==x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 c_1 e^{-x}+c_2 e^x}{2 x} \]