Internal problem ID [7096]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 367.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+(1+2/(1+3*x)^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (1+3 x \right )^{\frac {1}{3}} {\mathrm e}^{-x}+c_{2} \left (1+3 x \right )^{\frac {2}{3}} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 35
DSolve[y''[x]+2*y'[x]+(1+2/(1+3*x)^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \sqrt [3]{3 x+1} \left (c_2 \sqrt [3]{3 x+1}+c_1\right ) \\ \end{align*}