Internal problem ID [5266]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 23 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational]
\[ \boxed {4 y^{3} x^{3}+\left (3 y^{2} x^{4}-\frac {1}{y}\right ) y^{\prime }=-\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve((4*x^3*y(x)^3+1/x)+(3*x^4*y(x)^2-1/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {1}{\left (-\frac {3 x^{4}}{\operatorname {LambertW}\left (-3 c_{1} x^{7}\right )}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 4.154 (sec). Leaf size: 108
DSolve[(4*x^3*y[x]^3+1/x)+(3*x^4*y[x]^2-1/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-\frac {1}{3}} \sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{x^{4/3}} y(x)\to -\frac {\sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{\sqrt [3]{3} x^{4/3}} y(x)\to -\frac {(-1)^{2/3} \sqrt [3]{W\left (-3 e^{-3 c_1} x^7\right )}}{\sqrt [3]{3} x^{4/3}} y(x)\to 0 \end{align*}