Internal problem ID [6312]
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]]
\[ \boxed {y^{\prime \prime }+y^{\prime }=10 x^{4}+2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+diff(y(x),x)=10*x^4+2,y(x), singsol=all)
\[ y \left (x \right ) = -c_{1} {\mathrm e}^{-x}-120 x^{2}+40 x^{3}-10 x^{4}+2 x^{5}+242 x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 40
DSolve[y''[x]+y'[x]==10*x^4+2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^5-10 x^4+40 x^3-120 x^2+242 x-c_1 e^{-x}+c_2 \]