64.11.14 problem 14

Internal problem ID [13464]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 05:44:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=6*exp(-2*x)+3*exp(x)-4*x^2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} \left (\left (2 x^{2}+2 x +3\right ) {\mathrm e}^{2 x}+\left (c_{1} +x -\frac {1}{3}\right ) {\mathrm e}^{3 x}-2 x +c_{2} -\frac {2}{3}\right ) \]

✓ Solution by Mathematica

Time used: 1.658 (sec). Leaf size: 90

DSolve[D[y[x],{x,2}]+D[y[x],x]-2*y[x]==6*Exp[-2*x]+3*Exp[x]-4*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (\int _1^x\left (\frac {4}{3} e^{2 K[1]} K[1]^2-e^{3 K[1]}-2\right )dK[1]+e^{3 x} \int _1^x\left (-\frac {4}{3} e^{-K[2]} K[2]^2+2 e^{-3 K[2]}+1\right )dK[2]+c_2 e^{3 x}+c_1\right ) \]