20.1.32 problem Problem 40

Internal problem ID [3589]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 40
Date solved : Monday, January 27, 2025 at 07:46:48 AM
CAS classification : [[_2nd_order, _quadrature]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)=x*exp(x),y(0) = 3, D(y)(0) = 4],y(x), singsol=all)
 

\[ y \left (x \right ) = \left (x -2\right ) {\mathrm e}^{x}+5 x +5 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]==x*Exp[x],{y[0]==3,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x-2)+5 (x+1) \]