Internal problem ID [10241]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular
integral. Page 100
Problem number: Ex 3.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y-2 \,{\mathrm e}^{-x}+x^{2} {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=2*exp(-x)-x^2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \left (x^{2}-20\right ) \left (-x^{2}+2\right ) {\mathrm e}^{-x}}{60 x^{2}-120}+c_{1} {\mathrm e}^{-x}+c_{2} x \,{\mathrm e}^{-x}+c_{3} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 41
DSolve[y'''[x]+3*y''[x]+3*y'[x]+y[x]==2*Exp[-x]-x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{60} e^{-x} \left (-x^5+20 x^3+60 c_3 x^2+60 c_2 x+60 c_1\right ) \\ \end{align*}