35.6.19 problem 19

Internal problem ID [6169]
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
Date solved : Monday, January 27, 2025 at 01:44:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = -2 \,{\mathrm e}^{-\frac {3 x}{2}} \cos \left (x \right ) \sin \left (x \right )+{\mathrm e}^{-\frac {x}{2}} \sin \left (x \right ) c_2 +4 \cos \left (x \right )^{2} {\mathrm e}^{-\frac {3 x}{2}}+{\mathrm e}^{-\frac {x}{2}} \cos \left (x \right ) c_1 -2 \,{\mathrm e}^{-\frac {3 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 42

DSolve[4*D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==40*Exp[-3*x/2]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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