35.6.26 problem 26

Internal problem ID [6176]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 26
Date solved : Monday, January 27, 2025 at 01:46:36 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=8 x \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+y(x)=8*x*sin(x),y(x), singsol=all)
 

\[ y = \left (-2 x^{2}+c_1 \right ) \cos \left (x \right )+2 \sin \left (x \right ) \left (x +\frac {c_2}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+y[x]==8*x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-2 x^2+1+c_1\right ) \cos (x)+(2 x+c_2) \sin (x) \]