26.3.3 problem 2(c)

Internal problem ID [4263]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 08:46:51 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 5.253 (sec). Leaf size: 133

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

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x -\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \left (x \right ) &= \frac {\sqrt {6}\, \sqrt {x c_{1} \left (x -\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {6}\, \sqrt {x c_{1} \left (x +\sqrt {12 c_{1}^{2}+x^{2}}\right )}}{6 x c_{1}} \\ y \left (x \right ) &= \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: 10.112 (sec). Leaf size: 166

DSolve[(x+3*x^3*y[x]^4)*D[y[x],x]+y[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*}