Internal problem ID [2232]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime }=\sin \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x$3)+2*diff(y(x),x)=x^2*sin(x),y(x), singsol=all)
\[ y = -\cos \left (x \right ) x^{2}+8 \cos \left (x \right )-2 x \sin \left (x \right )+\frac {\sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) c_{1}}{2}-\frac {\sqrt {2}\, \cos \left (\sqrt {2}\, x \right ) c_{2}}{2}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 55
DSolve[y'''[x]+2*y'[x]==x^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\left (x^2-8\right ) \cos (x)-2 x \sin (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \]