Internal problem ID [13680]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-6 \,{\mathrm e}^{4 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-6*exp(4*x),y(0) = 6, D(y)(0) = 8],y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \,{\mathrm e}^{7 x}+{\mathrm e}^{6 x}+3\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 25
DSolve[{y''[x]-3*y'[x]-10*y[x]==-6*Exp[4*x],{y[0]==6,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (e^{6 x}+2 e^{7 x}+3\right ) \]