28.2.41 problem 41

Internal problem ID [4484]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 41
Date solved : Monday, January 27, 2025 at 09:21:04 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-diff(y(x),x)=exp(x)*(10+x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x^{3}-3 x^{2}+3 c_{1} +36 x -36\right ) {\mathrm e}^{x}}{3}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 31

DSolve[D[y[x],{x,2}]-D[y[x],x]==Exp[x]*(10+x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\frac {x^3}{3}-x^2+12 x-12+c_1\right )+c_2 \]