Internal problem ID [13385]
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: 22.4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y=-4 \cos \left (x \right )+7 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = -5] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-4*cos(x)+7*sin(x),y(0) = 8, D(y)(0) = -5],y(x), singsol=all)
\[ y = \frac {\left (\left (\cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{2 x}+3 \,{\mathrm e}^{7 x}+12\right ) {\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 30
DSolve[{y''[x]-3*y'[x]-10*y[x]==-4*Cos[x]+7*Sin[x],{y[0]==8,y'[0]==-5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (3 e^{-2 x} \left (e^{7 x}+4\right )-\sin (x)+\cos (x)\right ) \]