58.1.35 problem 35

Internal problem ID [9106]
Book : Second order enumerated odes
Section : section 1
Problem number : 35
Date solved : Monday, January 27, 2025 at 05:41:59 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+diff(y(x),x)=1+x+x^2+x^3,y(x), singsol=all)
 

\[ y = \frac {x^{4}}{4}-c_{1} {\mathrm e}^{-x}+\frac {5 x^{2}}{2}-\frac {2 x^{3}}{3}-4 x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]+D[y[x],x]==1+x+x^2+x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4}{4}-\frac {2 x^3}{3}+\frac {5 x^2}{2}-4 x-c_1 e^{-x}+c_2 \]