75.18.3 problem 592

Internal problem ID [17091]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 592
Date solved : Tuesday, January 28, 2025 at 09:52:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = 2 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 12

DSolve[{D[y[x],{x,2}]+9*y[x]==36*Exp[3*x],{y[0]==2,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{3 x} \]