35.8.7 problem 7

Internal problem ID [6214]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:48:10 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 85

dsolve(3*x^3*y(x)^2*diff(y(x),x)-x^2*y(x)^3=1,y(x), singsol=all)
 

\begin{align*} y &= \frac {3^{{2}/{3}} \left (3 c_{1} x^{4}-x \right )^{{1}/{3}}}{3 x} \\ y &= -\frac {3^{{2}/{3}} \left (3 c_{1} x^{4}-x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{6 x} \\ y &= \frac {\left (3 i 3^{{1}/{6}}-3^{{2}/{3}}\right ) \left (3 c_{1} x^{4}-x \right )^{{1}/{3}}}{6 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.789 (sec). Leaf size: 85

DSolve[3*x^3*y[x]^2*D[y[x],x]-x^2*y[x]^3==1,y[x],x,IncludeSingularSolutions -> True]
 

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