49.6.5 problem 1(e)

Internal problem ID [7633]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:08:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=3 \,{\mathrm e}^{-x}+2 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=3*exp(-x)+2*x^2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {3 \,{\mathrm e}^{-x}}{10}+\frac {2 x^{2}}{5}+\frac {16 x}{25}+\frac {44}{125} \]

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==3*Exp[-x]+2*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{250} \left (100 x^2+160 x+75 e^{-x}+88\right )+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x) \]