81.5.20 problem 20

Internal problem ID [18683]
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 : 20
Date solved : Tuesday, January 28, 2025 at 12:09:31 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \sin \left (\frac {\sqrt {P}\, x}{\sqrt {e}}\right ) c_{2} +\cos \left (\frac {\sqrt {P}\, x}{\sqrt {e}}\right ) c_{1} +a \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 39

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

\[ y(x)\to a+c_1 \cos \left (\frac {\sqrt {P} x}{\sqrt {e}}\right )+c_2 \sin \left (\frac {\sqrt {P} x}{\sqrt {e}}\right ) \]