64.11.25 problem 25

Internal problem ID [13475]
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 : 25
Date solved : Tuesday, January 28, 2025 at 05:44:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=9*x^2+4,y(0) = 6, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = -6 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{3 x}+3 x^{2}+8 x +10 \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 27

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==9*x^2+4,{y[0]==6,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^2+8 x-6 e^x+2 e^{3 x}+10 \]