Internal problem ID [4618]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.16, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=x \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+4*y(x)=x*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-x^{2}+8 c_{1} \right ) \cos \left (2 x \right )}{8}+\frac {\sin \left (2 x \right ) \left (16 c_{2} +x \right )}{16} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 38
DSolve[y''[x]+4*y[x]==x*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} \left (\left (-8 x^2+1+64 c_1\right ) \cos (2 x)+4 (x+16 c_2) \sin (2 x)\right ) \]