82.31.2 problem Ex. 2

Internal problem ID [18890]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 79
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:33:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -{\mathrm e}^{-2 x} \left (\frac {\left (7 \cos \left (x \right )-11 \sin \left (x \right )\right ) {\mathrm e}^{4 x}}{170}-c_{2} {\mathrm e}^{x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 40

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

\[ y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+\frac {1}{170} e^{2 x} (11 \sin (x)-7 \cos (x)) \]