50.10.11 problem 1(k)

Internal problem ID [7980]
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)
Date solved : Monday, January 27, 2025 at 03:35:08 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 40

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

\[ y(x)\to 2 x^5-10 x^4+40 x^3-120 x^2+242 x-c_1 e^{-x}+c_2 \]