Internal problem ID [11800]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+4 y=16 x +20 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+5*diff(y(x),x)+4*y(x)=16*x+20*exp(x),y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = 3 \,{\mathrm e}^{-x}-5+2 \,{\mathrm e}^{x}+4 x \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 22
DSolve[{y''[x]+5*y'[x]+4*y[x]==16*x+20*Exp[x],{y[0]==0,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 x+3 e^{-x}+2 e^x-5 \]