71.9.15 problem 17

Internal problem ID [14494]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 06:42:32 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=27 x +18 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=23\\ y^{\prime }\left (0\right )&=21 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+9*y(x)=27*x+18,y(0) = 23, D(y)(0) = 21],y(x), singsol=all)
 

\[ y = 6 \sin \left (3 x \right )+21 \cos \left (3 x \right )+2+3 x \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 22

DSolve[{D[y[x],{x,2}]+9*y[x]==27*x+18,{y[0]==23,Derivative[1][y][0] ==21}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x+6 \sin (3 x)+21 \cos (3 x)+2 \]