50.6.3 problem 1(c)

Internal problem ID [7895]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page 32
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:31:31 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.099 (sec). Leaf size: 133

dsolve(x*diff(y(x),x)+y(x)+3*x^3*y(x)^4*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x -\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y &= \frac {\sqrt {6}\, \sqrt {x c_{1} \left (x -\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y &= -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y &= \frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 10.211 (sec). Leaf size: 166

DSolve[x*D[y[x],x]+y[x]+3*x^3*y[x]^4*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {c_1-\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {c_1-\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}}}{\sqrt {3}} \\ y(x)\to -\frac {\sqrt {\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}+c_1}}{\sqrt {3}} \\ y(x)\to \frac {\sqrt {\frac {\sqrt {x^2 \left (3+c_1{}^2 x^2\right )}}{x^2}+c_1}}{\sqrt {3}} \\ y(x)\to 0 \\ \end{align*}