35.6.30 problem 36

Internal problem ID [6180]
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 : 36
Date solved : Monday, January 27, 2025 at 01:46:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right )+4 x \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x$2)+y(x)=2*sin(x)+4*x*cos(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]+y[x]==2*Sin[x]+4*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

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