Internal problem ID [4825]
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]]
\[ \boxed {4 y^{\prime \prime }+4 y^{\prime }+5 y=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
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)
\[ y \left (x \right ) = 4 \cos \left (x \right )^{2} {\mathrm e}^{-\frac {3 x}{2}}-2 \,{\mathrm e}^{-\frac {3 x}{2}} \cos \left (x \right ) \sin \left (x \right )+{\mathrm e}^{-\frac {x}{2}} \cos \left (x \right ) c_{1} +{\mathrm e}^{-\frac {x}{2}} \sin \left (x \right ) c_{2} -2 \,{\mathrm e}^{-\frac {3 x}{2}} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 42
DSolve[4*y''[x]+4*y'[x]+5*y[x]==40*Exp[-3*x/2]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x/2} \left (2 \cos (2 x)+c_1 e^x \sin (x)+\cos (x) \left (-2 \sin (x)+c_2 e^x\right )\right ) \]