Internal problem ID [4611]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.8, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=8+6*exp(x)+2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-2 x} \left (\left (-4+\frac {3 \cos \left (x \right )}{5}-\frac {\sin \left (x \right )}{5}\right ) {\mathrm e}^{2 x}-c_{2} {\mathrm e}^{x}+c_{1} -{\mathrm e}^{3 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 38
DSolve[y''[x]+3*y'[x]+2*y[x]==8+6*Exp[x]+2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x+\frac {\sin (x)}{5}-\frac {3 \cos (x)}{5}+c_1 e^{-2 x}+c_2 e^{-x}+4 \]