7.11.36 problem 37

Internal problem ID [357]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 37
Date solved : Monday, January 27, 2025 at 02:46:34 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=1+x \,{\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 24

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

\[ y = \frac {\left (x^{3}-3 x^{2}+18 x -24\right ) {\mathrm e}^{x}}{6}+x +4 \]

✓ Solution by Mathematica

Time used: 0.257 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{6} e^x \left (x^3-3 x^2+18 x-24\right )+x+4 \]