36.3.16 problem 17

Internal problem ID [6337]
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
Date solved : Monday, January 27, 2025 at 01:56:53 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve(1/y(x)-(3*y(x)-x/y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ -\frac {c_1}{y}+x -\frac {3 y^{3}}{4} = 0 \]

✓ Solution by Mathematica

Time used: 36.497 (sec). Leaf size: 870

DSolve[1/y[x]-(3*y[x]-x/y[x]^2)*D[y[x],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*}