69.1.107 problem 154

Internal problem ID [14260]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 154
Date solved : Tuesday, January 28, 2025 at 06:23:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+9 y&=6 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+9*y(x)=6*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{3 x}}{3}+c_1 \cos (3 x)+c_2 \sin (3 x) \]