73.15.25 problem 22.9 (c)

Internal problem ID [15456]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.9 (c)
Date solved : Tuesday, January 28, 2025 at 07:56:31 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = -\frac {x^{2}}{16}+\frac {x^{3}}{12}-\frac {c_{1} {\mathrm e}^{-4 x}}{4}+\frac {x}{32}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.137 (sec). Leaf size: 44

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

\[ y(x)\to \int _1^xe^{-4 K[2]} \left (c_1+\int _1^{K[2]}e^{4 K[1]} K[1]^2dK[1]\right )dK[2]+c_2 \]