73.14.3 problem 21.6 (i)

Internal problem ID [15413]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.6 (i)
Date solved : Tuesday, January 28, 2025 at 07:54:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 32

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

\[ y = \frac {\left (-12 x^{2} {\mathrm e}^{4 x}+{\mathrm e}^{6 x}-6 \,{\mathrm e}^{4 x} x -1\right ) {\mathrm e}^{-4 x}}{12} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{12} e^{-4 x} \left (-6 e^{4 x} x (2 x+1)+e^{6 x}-1\right ) \]