Internal problem ID [15361]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 592.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y=36 \,{\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)+9*y(x)=36*exp(3*x),y(0) = 2, D(y)(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = 2 \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 12
DSolve[{y''[x]+9*y[x]==36*Exp[3*x],{y[0]==2,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{3 x} \]