29.21.13 problem 589

Internal problem ID [5183]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 589
Date solved : Monday, January 27, 2025 at 10:18:19 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 51

dsolve(3*x^4*y(x)*diff(y(x),x) = 1-2*x^3*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {5}\, \sqrt {x^{{17}/{3}} \left (-2+5 x^{{5}/{3}} c_{1} \right )}}{5 x^{{13}/{3}}} \\ y \left (x \right ) &= \frac {\sqrt {5}\, \sqrt {x^{{17}/{3}} \left (-2+5 x^{{5}/{3}} c_{1} \right )}}{5 x^{{13}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.738 (sec). Leaf size: 51

DSolve[3 x^4 y[x] D[y[x],x]==1-2 x^3 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \\ y(x)\to \sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \\ \end{align*}