40.10.8 problem 17

Internal problem ID [6730]
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 : 17
Date solved : Monday, January 27, 2025 at 02:25:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 38

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

\[ y = \sin \left (x \right ) {\mathrm e}^{-x} c_2 +\cos \left (x \right ) {\mathrm e}^{-x} c_1 +\frac {x^{2}}{2}-x +\frac {1}{2}-\frac {2 \cos \left (x \right )}{5}+\frac {\sin \left (x \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.282 (sec). Leaf size: 50

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

\[ y(x)\to \frac {1}{10} e^{-x} \left (5 e^x (x-1)^2+\left (-4 e^x+10 c_2\right ) \cos (x)+2 \left (e^x+5 c_1\right ) \sin (x)\right ) \]