Internal problem ID [2227]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime }=x^{2}+\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$3)+2*diff(y(x),x)=x^2+cos(x),y(x), singsol=all)
\[ y = \frac {x^{3}}{6}+\frac {\sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) c_{1}}{2}-\frac {\sqrt {2}\, \cos \left (\sqrt {2}\, x \right ) c_{2}}{2}+\sin \left (x \right )-\frac {x}{2}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.417 (sec). Leaf size: 55
DSolve[y'''[x]+2*y'[x]==x^2+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{6}-\frac {x}{2}+\sin (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \]