71.12.3 problem 3

Internal problem ID [14519]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.5, page 221
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 06:42:55 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 19

dsolve([diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=2*exp(x),y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = -3],y(x), singsol=all)
 

\[ y = \left (x -2\right ) {\mathrm e}^{x}+3 \cos \left (x \right )+4 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 21

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

\[ y(x)\to e^x (x-2)+4 \sin (x)+3 \cos (x) \]