Internal problem ID [241]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 46.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=x \cos \left (x \right )^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+y(x)=x*cos(x)^3,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\frac {\left (12 x^{2}+6 \cos \left (x \right )^{2}+9\right ) \sin \left (x \right )}{64}-\frac {x \cos \left (x \right )^{3}}{8}+\frac {9 \cos \left (x \right ) x}{32} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 49
DSolve[y''[x]+y[x]==x*Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{128} \left (\sin (x) \left (24 x^2+6 \cos (2 x)-9+128 c_2\right )-4 x \cos (3 x)+8 (3 x+16 c_1) \cos (x)\right ) \]