85.1.19 problem 11 (e)

Internal problem ID [22424]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 11 (e)
Date solved : Thursday, October 02, 2025 at 08:39:11 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=12 x \left (4-x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=7 \\ y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x) = 12*x*(-x+4); 
ic:=[y(0) = 7, y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -x^{4}+8 x^{3}-14 x +7 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 20

ode=D[y[x],{x,2}]==12*x*(4-x); 
ic={y[0]==7,y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x^4+8 x^3-14 x+7 \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*x*(4 - x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 7, y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - x^{4} + 8 x^{3} - 14 x + 7 \]