15.14.26 problem 26

Internal problem ID [3198]
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 : 26
Date solved : Monday, January 27, 2025 at 07:25:53 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

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

\[ y = \frac {x^{3}}{6}-\frac {c_2 \sqrt {2}\, \cos \left (\sqrt {2}\, x \right )}{2}+\frac {\sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) c_{1}}{2}+\sin \left (x \right )-\frac {x}{2}+c_3 \]

✓ Solution by Mathematica

Time used: 0.435 (sec). Leaf size: 55

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

\[ y(x)\to \frac {x^3}{6}-\frac {x}{2}+\sin (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \]