29.35.5 problem 1037

Internal problem ID [5603]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1037
Date solved : Monday, January 27, 2025 at 12:13:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.137 (sec). Leaf size: 47

dsolve(diff(y(x),x)^3-x*y(x)^4*diff(y(x),x)-y(x)^5 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y \left (x \right ) &= \frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \sqrt {\frac {c_{1}^{10}}{\left (c_{1}^{4} x -1\right )^{2}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 64

DSolve[(D[y[x],x])^3 -x*y[x]^4*D[y[x],x]- y[x]^5==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{c_1 x-c_1{}^3} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 \sqrt {3}}{2 x^{3/2}} \\ y(x)\to \frac {3 \sqrt {3}}{2 x^{3/2}} \\ \end{align*}