73.15.38 problem 22.10 (k)

Internal problem ID [15469]
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 : 22.10 (k)
Date solved : Tuesday, January 28, 2025 at 07:57:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=10*x^2+4*x+8,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +2 x^{2}+4 x +4 \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==10*x^2+4*x+8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x^2+4 x+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x)+4 \]