62.24.3 problem Ex 3

Internal problem ID [12931]
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
Date solved : Tuesday, January 28, 2025 at 04:44:16 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=2 \,{\mathrm e}^{-x}-x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = -\frac {{\mathrm e}^{-x} \left (x^{5}-60 x^{2} c_3 -20 x^{3}-60 c_{2} x -60 c_{1} \right )}{60} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 41

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+y[x]==2*Exp[-x]-x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{60} e^{-x} \left (-x^5+20 x^3+60 c_3 x^2+60 c_2 x+60 c_1\right ) \]