8.11.23 problem 46

Internal problem ID [891]
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
Date solved : Wednesday, February 05, 2025 at 04:43:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=x \cos \left (x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

dsolve(diff(y(x),x$2)+y(x)=x*cos(x)^3,y(x), singsol=all)
 

\[ y = -\frac {x \cos \left (x \right )^{3}}{8}+\frac {3 \sin \left (x \right ) \cos \left (x \right )^{2}}{32}+\frac {\left (9 x +32 c_1 \right ) \cos \left (x \right )}{32}+\frac {3 \left (x^{2}+\frac {16 c_2}{3}+\frac {3}{4}\right ) \sin \left (x \right )}{16} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 49

DSolve[D[y[x],{x,2}]+y[x]==x*Cos[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{128} \left (\sin (x) \left (24 x^2+6 \cos (2 x)-9+128 c_2\right )-4 x \cos (3 x)+8 (3 x+16 c_1) \cos (x)\right ) \]