Internal problem ID [13700]
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: 22.2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-5 \,{\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-5*exp(3*x),y(0) = 5, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (3 \,{\mathrm e}^{7 x}+{\mathrm e}^{5 x}+6\right ) {\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 28
DSolve[{y''[x]-3*y'[x]-10*y[x]==-5*Exp[3*x],{y[0]==5,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (e^{5 x}+3 e^{7 x}+6\right ) \]