Internal problem ID [13687]
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: 21.13 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-18*exp(4*x)+14*exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (14 x +7 c_{2} -2\right ) {\mathrm e}^{7 x}}{7}+c_{1} +3 \,{\mathrm e}^{6 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 36
DSolve[y''[x]-3*y'[x]-10*y[x]==-18*Exp[4*x]+14*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{4 x}+c_1 e^{-2 x}+e^{5 x} \left (2 x-\frac {2}{7}+c_2\right ) \]