Internal problem ID [12524]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+9 y=6 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+9*y(x)=6*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )+\frac {{\mathrm e}^{3 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 29
DSolve[y''[x]+9*y[x]==6*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{3 x}}{3}+c_1 \cos (3 x)+c_2 \sin (3 x) \]