15.11.6 problem 6

Internal problem ID [3116]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:20:28 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 37

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

\[ y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_2 +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +x^{2}-2 x \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 54

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

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