15.15.10 problem 11

Internal problem ID [3214]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:26:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

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

\[ y = -{\mathrm e}^{-2 x} c_{1} +c_2 \,{\mathrm e}^{-x}+\frac {\left (25 x^{2}+60 x -133\right ) \cos \left (x \right )}{250}+\frac {\sin \left (x \right ) \left (75 x^{2}-170 x +81\right )}{250} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 53

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

\[ y(x)\to \frac {1}{250} \left (\left (75 x^2-170 x+81\right ) \sin (x)+\left (25 x^2+60 x-133\right ) \cos (x)\right )+c_1 e^{-2 x}+c_2 e^{-x} \]