Internal problem ID [13792]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.2 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=12 \,{\mathrm e}^{2 x}} \] 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: 23
dsolve([diff(y(x),x$2)-diff(y(x),x)-6*y(x)=12*exp(2*x),y(0) = 0, D(y)(0) = 8],y(x), singsol=all)
\[ y \left (x \right ) = \left (4 \,{\mathrm e}^{5 x}-3 \,{\mathrm e}^{4 x}-1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 27
DSolve[{y''[x]-y'[x]-6*y[x]==12*Exp[2*x],{y[0]==0,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (-3 e^{4 x}+4 e^{5 x}-1\right ) \]