15.14.31 problem 33

Internal problem ID [3203]
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 : 33
Date solved : Monday, January 27, 2025 at 07:25:56 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 46

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

\[ y = -\frac {c_2 \sqrt {2}\, \cos \left (\sqrt {2}\, x \right )}{2}+\frac {\sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) c_{1}}{2}-x^{2} \cos \left (x \right )+8 \cos \left (x \right )-2 x \sin \left (x \right )+c_3 \]

✓ Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 55

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

\[ y(x)\to -\left (x^2-8\right ) \cos (x)-2 x \sin (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \]