59.1.360 problem 367

Internal problem ID [9532]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 367
Date solved : Monday, January 27, 2025 at 06:03:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+(1+2/(1+3*x)^2)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \left (3 x +1\right )^{{1}/{3}} \left (\left (3 x +1\right )^{{1}/{3}} c_{2} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+(1+2/(1+3*x)^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \sqrt [3]{3 x+1} \left (c_2 \sqrt [3]{3 x+1}+c_1\right ) \]