10.11 problem 1(k)

Internal problem ID [5559]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number: 1(k).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_y]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }-10 x^{4}-2=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+diff(y(x),x)=10*x^4+2,y(x), singsol=all)
 

\[ y \relax (x ) = -{\mathrm e}^{-x} c_{1}-120 x^{2}+40 x^{3}-10 x^{4}+2 x^{5}+242 x +c_{2} \]

Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 35

DSolve[y''[x]+y'[x]==10*x^4+2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 x (x (x ((x-5) x+20)-60)+121)-c_1 e^{-x}+c_2 \\ \end{align*}