81.5.16 problem 16

Internal problem ID [18679]
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 : 16
Date solved : Tuesday, January 28, 2025 at 12:09:22 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} e y^{\prime \prime }&=\frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(e*diff(y(x),x$2)=w/2*(L^2/4-x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {w \left (3 L^{2}-4 x^{2}\right )^{2}}{384 e}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 34

DSolve[e*D[y[x],{x,2}]==w/2*(L^2/4-x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {w x^2 \left (3 L^2-2 x^2\right )}{48 e}+c_2 x+c_1 \]