Internal problem ID [11802]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y=4 x \,{\mathrm e}^{-3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)+7*diff(y(x),x)+10*y(x)=4*x*exp(-3*x),y(0) = 0, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x}+\left (-2 x -1\right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 19
DSolve[{y''[x]+7*y'[x]+10*y[x]==4*x*Exp[-3*x],{y[0]==0,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (-2 x+e^x-1\right ) \]