58.1.34 problem 34

Internal problem ID [9105]
Book : Second order enumerated odes
Section : section 1
Problem number : 34
Date solved : Monday, January 27, 2025 at 05:41:56 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+diff(y(x),x)=1+x+x^2,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}-c_{1} {\mathrm e}^{-x}-\frac {x^{2}}{2}+2 x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+D[y[x],x]==1+x+x^2,y[x],x,IncludeSingularSolutions -> True]
 

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