82.12.19 problem Ex. 21

Internal problem ID [18784]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 21
Date solved : Tuesday, January 28, 2025 at 12:17:19 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=x^{3} y^{3}-y x \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(diff(y(x),x)=x^3*y(x)^3-x*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.292 (sec). Leaf size: 50

DSolve[D[y[x],x]==x^3*y[x]^3-x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x^2+c_1 e^{x^2}+1}} \\ y(x)\to \frac {1}{\sqrt {x^2+c_1 e^{x^2}+1}} \\ y(x)\to 0 \\ \end{align*}