15.14.8 problem 8

Internal problem ID [3180]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 8
Date solved : Monday, January 27, 2025 at 07:25:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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

\[ y = -{\mathrm e}^{-2 x} \left (\frac {\left (-\sin \left (x \right )+\cos \left (x \right )\right ) {\mathrm e}^{3 x}}{10}-c_2 \,{\mathrm e}^{x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 36

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

\[ y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+\frac {1}{10} e^x (\sin (x)-\cos (x)) \]