85.28.1 problem 1

Internal problem ID [22608]
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 60
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:55:00 PM
CAS classification : [[_high_order, _quadrature]]

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

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 31

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

\[ y = -\frac {25 x^{4}}{288}+\frac {x^{4} \ln \left (x \right )}{24}+\frac {x^{3}}{6}-\frac {x^{2}}{8}+\frac {x}{18}-\frac {1}{96} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to \frac {1}{288} \left (-25 x^4+12 x^4 \log (x)+48 x^3-36 x^2+16 x-3\right ) \end{align*}

✓ Sympy. Time used: 0.224 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-log(x) + Derivative(y(x), (x, 4)),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 0, Subs(Derivative(y(x), (x, 2)), x, 1): 0, Subs(Derivative(y(x), (x, 3)), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{4} \log {\left (x \right )}}{24} - \frac {25 x^{4}}{288} + \frac {x^{3}}{6} - \frac {x^{2}}{8} + \frac {x}{18} - \frac {1}{96} \]