82.48.20 problem Ex. 20

Internal problem ID [19001]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 20
Date solved : Tuesday, January 28, 2025 at 12:44:54 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)=f(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \int \left (\int \left (\int f \left (x \right )d x \right )d x +c_{1} x \right )d x +c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 43

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

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