Internal problem ID [15299]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 529.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=4 \cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+y(x)=4*x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+c_{2} -1\right ) \sin \left (x \right )+\cos \left (x \right ) \left (x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 30
DSolve[y''[x]+y[x]==4*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (2 x^2-1+2 c_2\right ) \sin (x)+(x+c_1) \cos (x) \]