Internal problem ID [15186]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 328.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _quadrature]]
\[ \boxed {y^{\prime \prime \prime }=x +\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)=x+cos(x),y(x), singsol=all)
\[ y = \frac {x^{4}}{24}+\frac {c_{1} x^{2}}{2}-\sin \left (x \right )+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 29
DSolve[y'''[x]==x+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{24}+c_3 x^2-\sin (x)+c_2 x+c_1 \]