Internal problem ID [4486]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page
64
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 18
dsolve(1/y(x)-(3*y(x)-x/y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {c_{1}}{y \relax (x )}+x -\frac {3 y \relax (x )^{3}}{4} = 0 \]
✓ Solution by Mathematica
Time used: 13.963 (sec). Leaf size: 870
DSolve[1/y[x]-(3*y[x]-x/y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt {-\frac {2 \sqrt {6} x}{\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}-\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}-\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {-\frac {2 \sqrt {6} x}{\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}-\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}-\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}-\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}-\sqrt {\frac {2 \sqrt {6} x}{\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}-\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}-\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt {\frac {2 \sqrt {6} x}{\sqrt {\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}+\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}-\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}-\frac {4 c_1}{\sqrt [3]{3 x^2-\sqrt {9 x^4-64 c_1{}^3}}}}}{\sqrt {6}} \\ \end{align*}