81.5.18 problem 18

Internal problem ID [18681]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 12:09:26 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} e y^{\prime \prime }&=-P \left (L -x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

dsolve(e*diff(y(x),x$2)=-P*(L-x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (6 c_{1} x +6 c_{2} \right ) e -3 P \left (L -\frac {x}{3}\right ) x^{2}}{6 e} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 28

DSolve[e*D[y[x],{x,2}]==-P*(L-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {P x^2 (x-3 L)}{6 e}+c_2 x+c_1 \]