82.40.3 problem Ex. 3

Internal problem ID [18949]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 94
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:38:10 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(x*diff(y(x),x$2)+2*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 34

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

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