15.8.43 problem 45

Internal problem ID [3046]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 45
Date solved : Sunday, March 30, 2025 at 01:13:52 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=x^{4}+4 y \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 10

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

\[ y = \ln \left (x \right ) x^{4} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 11

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

\[ y(x)\to x^4 \log (x) \]

✓ Sympy. Time used: 0.180 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x^{4} \log {\left (x \right )} \]