Internal problem ID [13356]
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: 21.5 (ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=24 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = -2, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+4*y(x)=24*exp(2*x),y(0) = -2, D(y)(0) = 2],y(x), singsol=all)
\[ y = -2 \sin \left (2 x \right )-5 \cos \left (2 x \right )+3 \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 25
DSolve[{y''[x]+4*y[x]==24*Exp[2*x],{y[0]==-2,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{2 x}-2 \sin (2 x)-5 \cos (2 x) \]