Internal problem ID [247]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 52.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+9*y(x)=sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} -\frac {x \cos \left (3 x \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{6}+c_1\right ) \cos (3 x)+\frac {1}{36} (1+36 c_2) \sin (3 x) \]