Internal problem ID [11801]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-8 y^{\prime }+15 y=9 \,{\mathrm e}^{2 x} x} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 10] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)-8*diff(y(x),x)+15*y(x)=9*x*exp(2*x),y(0) = 5, D(y)(0) = 10],y(x), singsol=all)
\[ y \left (x \right ) = -2 \,{\mathrm e}^{5 x}+3 \,{\mathrm e}^{3 x}+\left (3 x +4\right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 28
DSolve[{y''[x]-8*y'[x]+15*y[x]==9*x*Exp[2*x],{y[0]==5,y'[0]==10}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (3 x+3 e^x-2 e^{3 x}+4\right ) \]