82.54.7 problem Ex. 7

Internal problem ID [19023]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 7
Date solved : Tuesday, January 28, 2025 at 12:45:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+4*x^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]+4*x*D[y[x],x]+4*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-x \left (x+\sqrt {2}\right )} \left (\sqrt {2} c_2 e^{2 \sqrt {2} x}+4 c_1\right ) \]