Internal problem ID [4317]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+4 y^{\prime }+5 y-40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(4*diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=40*exp(-3*x/2)*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} \sin \relax (x ) c_{2}+{\mathrm e}^{-\frac {x}{2}} \cos \relax (x ) c_{1}+\left (-\sin \left (2 x \right )+2 \cos \left (2 x \right )\right ) {\mathrm e}^{-\frac {3 x}{2}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 41
DSolve[4*y''[x]+4*y'[x]+5*y[x]==40*Exp[-3*x/2]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x/2} \left (-\sin (2 x)+2 \cos (2 x)+e^x (c_2 \cos (x)+c_1 \sin (x))\right ) \\ \end{align*}