27.3 problem Ex 3

Internal problem ID [10251]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of undetermined coefficients. Page 107
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 }+y-2 \,{\mathrm e}^{x}-x^{3}+x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 21

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

\[ y \relax (x ) = \sin \relax (x ) c_{2}+\cos \relax (x ) c_{1}+x^{3}+{\mathrm e}^{x}-7 x \]

Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 25

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

\begin{align*} y(x)\to x^3-7 x+e^x+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}