Internal problem ID [6711]
Book: Second order enumerated odes
Section: section 2
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}-4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+(1-1/x)*diff(y(x),x)+4*x^2*y(x)*exp(-2*x)=4*(x^2+x^3)*exp(-3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 \left (x +1\right ) {\mathrm e}^{-x}\right ) c_{2}+\cos \left (2 \left (x +1\right ) {\mathrm e}^{-x}\right ) c_{1}+\left (x +1\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 44
DSolve[y''[x]+(1-1/x)*y'[x]+4*x^2*y[x]*Exp[-2*x]==4*(x^2+x^3)*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x+1)+c_1 \cos \left (2 e^{-x} (x+1)\right )-c_2 \sin \left (2 e^{-x} (x+1)\right ) \\ \end{align*}