29.24.12 problem 674

Internal problem ID [5265]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 674
Date solved : Monday, January 27, 2025 at 10:50:45 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.941 (sec). Leaf size: 157

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

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

✓ Solution by Mathematica

Time used: 13.616 (sec). Leaf size: 122

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

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