78.13.11 problem 1 (k)

Internal problem ID [18333]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (k)
Date solved : Tuesday, January 28, 2025 at 11:46:59 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 40

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

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