Internal problem ID [13397]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=39 \,{\mathrm e}^{2 x} x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve([diff(y(x),x$2)+9*y(x)=39*x*exp(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y = 3 x \,{\mathrm e}^{2 x}-\frac {5 \sin \left (3 x \right )}{13}+\frac {25 \cos \left (3 x \right )}{13}-\frac {12 \,{\mathrm e}^{2 x}}{13} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 34
DSolve[{y''[x]+9*y[x]==39*x*Exp[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{13} \left (3 e^{2 x} (13 x-4)-5 \sin (3 x)+25 \cos (3 x)\right ) \]