Internal problem ID [11806]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-10 y^{\prime }+29 y=8 \,{\mathrm e}^{5 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)-10*diff(y(x),x)+29*y(x)=8*exp(5*x),y(0) = 0, D(y)(0) = 8],y(x), singsol=all)
\[ y \left (x \right ) = -2 \,{\mathrm e}^{5 x} \left (-1-2 \sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 24
DSolve[{y''[x]-10*y'[x]+29*y[x]==8*Exp[5*x],{y[0]==0,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 e^{5 x} (-2 \sin (2 x)+\cos (2 x)-1) \]