62.29.3 problem Ex 3

Internal problem ID [12954]
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
Date solved : Tuesday, January 28, 2025 at 04:45:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*x^3-x*exp(3*x),y(x), singsol=all)
 

\[ y = -48+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}+\frac {\left (1-2 x \right ) {\mathrm e}^{3 x}}{32}+2 x^{3}-12 x^{2}+36 x \]

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 77

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

\[ y(x)\to e^{-x} \left (\int _1^x\left (e^{4 K[1]} K[1]^2-2 e^{K[1]} K[1]^4\right )dK[1]+x \int _1^x\left (2 e^{K[2]} K[2]^3-e^{4 K[2]} K[2]\right )dK[2]+c_2 x+c_1\right ) \]