15.14.32 problem 34

Internal problem ID [3204]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 34
Date solved : Monday, January 27, 2025 at 07:25:57 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 45

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

\[ y = c_4 \,{\mathrm e}^{-x}+\frac {\left (-3 x^{2}+8 c_{1} +2\right ) \cos \left (x \right )}{8}+\frac {\left (-2 x^{3}+24 c_3 +15 x \right ) \sin \left (x \right )}{24}+c_2 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 54

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

\[ y(x)\to \left (-\frac {x^3}{12}+\frac {5 x}{8}+c_4\right ) \sin (x)+\left (-\frac {3 x^2}{8}+\frac {5}{16}+c_2\right ) \cos (x)+c_1 e^x+c_3 e^{-x} \]