40.10.11 problem 20

Internal problem ID [6733]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 15. Linear equations with constant coefficients (Variation of parameters). Supplemetary problems. Page 98
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:25:38 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: 23

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

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

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 32

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

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