81.5.17 problem 17

Internal problem ID [18680]
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 : 17
Date solved : Tuesday, January 28, 2025 at 12:09:24 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

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

\[ y \left (x \right ) = \frac {-w \,x^{4}+\left (-2 w L -2 P \right ) x^{3}+24 c_{1} x e +24 c_{2} e}{24 e} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 33

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

\[ y(x)\to -\frac {x^3 (w (2 L+x)+2 P)}{24 e}+c_2 x+c_1 \]