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 : Monday, January 27, 2025 at 07:11:36 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*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

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

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

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