82.33.11 problem Ex. 11

Internal problem ID [18904]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 11
Date solved : Tuesday, January 28, 2025 at 12:34:03 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 46

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

\[ y \left (x \right ) = \frac {\left (-4 x^{4}+192 c_3 x +36 x^{2}+192 c_{1} -21\right ) \cos \left (x \right )}{192}+\frac {\sin \left (x \right ) \left (x^{3}+\left (12 c_4 -3\right ) x +12 c_{2} \right )}{12} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 56

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

\[ y(x)\to \frac {1}{12} \left (x^3+3 (-1+4 c_4) x+12 c_3\right ) \sin (x)+\left (-\frac {x^4}{48}+\frac {3 x^2}{16}+c_2 x-\frac {5}{32}+c_1\right ) \cos (x) \]