7.11.29 problem 30

Internal problem ID [350]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:46:15 AM
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: 0.006 (sec). Leaf size: 37

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

\[ y = \left (c_4 x +c_2 \right ) {\mathrm e}^{-x}+\frac {\left (x^{2}-4\right ) \cos \left (x \right )}{4}+\left (x c_3 +c_1 \right ) {\mathrm e}^{x}-x \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 52

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

\[ y(x)\to \frac {1}{4} \left (x^2-4\right ) \cos (x)-x \sin (x)+e^{-x} \left (c_2 x+c_3 e^{2 x}+c_4 e^{2 x} x+c_1\right ) \]