Internal problem ID [4319]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {5 y^{\prime \prime }+6 y^{\prime }+2 y-x^{2}-6 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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)
\[ y \relax (x ) = {\mathrm e}^{-\frac {3 x}{5}} \sin \left (\frac {x}{5}\right ) c_{2}+{\mathrm e}^{-\frac {3 x}{5}} \cos \left (\frac {x}{5}\right ) c_{1}+\frac {x^{2}}{2}-\frac {5}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 42
DSolve[5*y''[x]+6*y'[x]+2*y[x]==x^2+6*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x^2-5\right )+e^{-3 x/5} \left (c_2 \cos \left (\frac {x}{5}\right )+c_1 \sin \left (\frac {x}{5}\right )\right ) \\ \end{align*}