29.32.6 problem 940

Internal problem ID [5518]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 32
Problem number : 940
Date solved : Monday, January 27, 2025 at 11:35:04 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 2.140 (sec). Leaf size: 45

dsolve(x^8*diff(y(x),x)^2+3*x*diff(y(x),x)+9*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{4 x^{6}} \\ y \left (x \right ) &= \frac {-x^{3}+c_{1}}{x^{3} c_{1}^{2}} \\ y \left (x \right ) &= \frac {-x^{3}-c_{1}}{x^{3} c_{1}^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.663 (sec). Leaf size: 130

DSolve[x^8 (D[y[x],x])^2+3 x D[y[x],x]+9 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {Solve}\left [\frac {x \sqrt {4 x^6 y(x)-1} \arctan \left (\sqrt {4 x^6 y(x)-1}\right )}{3 \sqrt {x^2-4 x^8 y(x)}}-\frac {1}{6} \log (y(x))&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {\sqrt {x^2-4 x^8 y(x)} \arctan \left (\sqrt {4 x^6 y(x)-1}\right )}{3 x \sqrt {4 x^6 y(x)-1}}-\frac {1}{6} \log (y(x))&=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}