35.6.21 problem 21

Internal problem ID [6171]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 21
Date solved : Monday, January 27, 2025 at 01:45:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \end{align*}

✓ Solution by Maple

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

dsolve(5*diff(y(x),x$2)+6*diff(y(x),x)+2*y(x)=x^2+6*x,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {3 x}{5}} \sin \left (\frac {x}{5}\right ) c_2 +{\mathrm e}^{-\frac {3 x}{5}} \cos \left (\frac {x}{5}\right ) c_1 +\frac {x^{2}}{2}-\frac {5}{2} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 47

DSolve[5*D[y[x],{x,2}]+6*D[y[x],x]+2*y[x]==x^2+6*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (x^2-5\right )+c_2 e^{-3 x/5} \cos \left (\frac {x}{5}\right )+c_1 e^{-3 x/5} \sin \left (\frac {x}{5}\right ) \]