75.14.2 problem 328

Internal problem ID [16916]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 328
Date solved : Tuesday, January 28, 2025 at 09:40:50 AM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (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: 0.015 (sec). Leaf size: 46

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

\[ y(x)\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}(\cos (K[1])+K[1])dK[1]dK[2]dK[3]+x (c_3 x+c_2)+c_1 \]