29.30.30 problem 890

Internal problem ID [5470]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 890
Date solved : Monday, January 27, 2025 at 11:25:09 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 16 x {y^{\prime }}^{2}+8 y^{\prime } y+y^{6}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 101

dsolve(16*x*diff(y(x),x)^2+8*y(x)*diff(y(x),x)+y(x)^6 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{x^{{1}/{4}}} \\ y \left (x \right ) &= -\frac {1}{x^{{1}/{4}}} \\ y \left (x \right ) &= -\frac {i}{x^{{1}/{4}}} \\ y \left (x \right ) &= \frac {i}{x^{{1}/{4}}} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +4 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \sqrt {-\textit {\_a}^{4}+1}}d \textit {\_a} \right )\right )}{x^{{1}/{4}}} \\ y \left (x \right ) &= \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} -4 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \sqrt {-\textit {\_a}^{4}+1}}d \textit {\_a} \right )\right )}{x^{{1}/{4}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.601 (sec). Leaf size: 171

DSolve[16 x(D[y[x],x])^2+8 y[x] D[y[x],x]+y[x]^6==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {2} e^{\frac {c_1}{4}}}{\sqrt {x+e^{c_1}}} \\ y(x)\to -\frac {i \sqrt {2} e^{\frac {c_1}{4}}}{\sqrt {x+e^{c_1}}} \\ y(x)\to \frac {i \sqrt {2} e^{\frac {c_1}{4}}}{\sqrt {x+e^{c_1}}} \\ y(x)\to \frac {\sqrt {2} e^{\frac {c_1}{4}}}{\sqrt {x+e^{c_1}}} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{\sqrt [4]{x}} \\ y(x)\to -\frac {i}{\sqrt [4]{x}} \\ y(x)\to \frac {i}{\sqrt [4]{x}} \\ y(x)\to \frac {1}{\sqrt [4]{x}} \\ \end{align*}