76.1.1 problem 1

Internal problem ID [17300]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 09:59:02 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x)=x^4/y(x),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {10 x^{5}+25 c_{1}}}{5} \\ y &= \frac {\sqrt {10 x^{5}+25 c_{1}}}{5} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 50

DSolve[D[y[x],x]==x^4/y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {\frac {2}{5}} \sqrt {x^5+5 c_1} \\ y(x)\to \sqrt {\frac {2}{5}} \sqrt {x^5+5 c_1} \\ \end{align*}