Internal problem ID [10264]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-2 x^{3}+x \,{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*x^3-x*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+{\mathrm e}^{-x} x c_{1}+\frac {\left (-2 x +1\right ) {\mathrm e}^{3 x}}{32}+2 x^{3}-12 x^{2}+36 x -48 \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 44
DSolve[y''[x]+2*y'[x]+y[x]==2*x^3-x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{32} e^{3 x} (1-2 x)+2 x ((x-6) x+18)+e^{-x} (c_2 x+c_1)-48 \\ \end{align*}