81.5.19 problem 19

Internal problem ID [18682]
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 : 19
Date solved : Tuesday, January 28, 2025 at 12:09:29 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 50

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

\[ y \left (x \right ) = \frac {-w \,x^{4}+\left (4 w L +4 P \right ) x^{3}-6 L \left (w L +2 P \right ) x^{2}+24 c_{1} x e +24 c_{2} e}{24 e} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 47

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

\[ y(x)\to -\frac {x^2 \left (6 L^2 w+12 L P-4 L w x-4 P x+w x^2\right )}{24 e}+c_2 x+c_1 \]