83.27.18 problem 18

Internal problem ID [19364]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 01:35:30 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (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: 0.003 (sec). Leaf size: 43

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

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