59.1.445 problem 458

Internal problem ID [9617]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 458
Date solved : Monday, January 27, 2025 at 06:04:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (2+4 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

dsolve(x*diff(y(x),x$2)-(4*x+1)*diff(y(x),x)+(4*x+2)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 25

DSolve[x*D[y[x],{x,2}]-(4*x+1)*D[y[x],x]+(4*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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