Internal problem ID [2209]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\sin \left (x \right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -{\mathrm e}^{-2 x} \left (\frac {\left (-\sin \left (x \right )+\cos \left (x \right )\right ) {\mathrm e}^{3 x}}{10}-c_{2} {\mathrm e}^{x}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 36
DSolve[y''[x]+3*y'[x]+2*y[x]==Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+\frac {1}{10} e^x (\sin (x)-\cos (x)) \]