85.34.8 problem 8

Internal problem ID [22716]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 67
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:11:48 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime }+24 x \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 2*diff(diff(diff(y(x),x),x),x)+24*x; 
ic:=[y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3 \,{\mathrm e}^{2 x}}{4}-x^{3}-\frac {x^{4}}{2}-\frac {3 x^{2}}{2}-\frac {3 x}{2}+\frac {1}{4} \]

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 36

ode=D[y[x],{x,4}]==2*D[y[x],{x,3}]+24*x; 
ic={y[0]==1,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (-2 x^4-4 x^3-6 x^2-6 x+3 e^{2 x}+1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x + 3*y(x)) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out