59.1.633 problem 650

Internal problem ID [9805]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 650
Date solved : Monday, January 27, 2025 at 06:14:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2+6)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+4*x*D[y[x],x]+(4*x^2+6)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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