38.2.8 problem 8

Internal problem ID [6437]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 8
Date solved : Monday, January 27, 2025 at 02:03:08 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{3}+y^{3}&=3 x y^{2} y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 72

dsolve((x^3+y(x)^3)=3*x*y(x)^2*diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= \frac {2^{{2}/{3}} {\left (x \left (x^{2}+2 c_1 \right )\right )}^{{1}/{3}}}{2} \\ y &= -\frac {2^{{2}/{3}} {\left (x \left (x^{2}+2 c_1 \right )\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {2^{{2}/{3}} {\left (x \left (x^{2}+2 c_1 \right )\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 90

DSolve[(x^3+y[x]^3)==3*x*y[x]^2*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt [3]{-\frac {1}{2}} \sqrt [3]{x} \sqrt [3]{x^2+2 c_1} \\ y(x)\to \frac {\sqrt [3]{x} \sqrt [3]{x^2+2 c_1}}{\sqrt [3]{2}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{x} \sqrt [3]{x^2+2 c_1}}{\sqrt [3]{2}} \\ \end{align*}