83.23.21 problem 21

Internal problem ID [19302]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 01:25:17 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 47

dsolve(diff(y(x),x)^3=y(x)^4*(y(x)+x*diff(y(x),x)),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: 0.031 (sec). Leaf size: 64

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