Internal problem ID [11255]
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]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x} \left (x^{5}-60 c_{2} x^{2}-20 x^{3}-60 c_{3} x -60 c_{1} \right )}{60} \]
✓ Solution by Mathematica
Time used: 0.017 (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]
\[ y(x)\to \frac {1}{60} e^{-x} \left (-x^5+20 x^3+60 c_3 x^2+60 c_2 x+60 c_1\right ) \]