Internal problem ID [13361]
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: 21.9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=7 \,{\mathrm e}^{5 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 12, y^{\prime }\left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=7*exp(5*x),y(0) = 12, D(y)(0) = -2],y(x), singsol=all)
\[ y = \left (9+\left (x +3\right ) {\mathrm e}^{7 x}\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 22
DSolve[{y''[x]-3*y'[x]-10*y[x]==7*Exp[5*x],{y[0]==12,y'[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (e^{7 x} (x+3)+9\right ) \]