75.16.39 problem 512

Internal problem ID [17012]
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. Trial and error method. Exercises page 132
Problem number : 512
Date solved : Tuesday, January 28, 2025 at 09:45:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+9 y&=9 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)+9*y(x)=9,y(x), singsol=all)
 

\[ y = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +1 \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]+9*y[x]==9,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos (3 x)+c_2 \sin (3 x)+1 \]