Internal problem ID [3953]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 707.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (x^{3}-y^{4}\right ) y^{\prime }-3 x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 25
dsolve((x^3-y(x)^4)*diff(y(x),x) = 3*x^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (x^{9} \textit {\_Z}^{4}+3-{\mathrm e}^{\frac {9 c_{1}}{4}} \textit {\_Z} \right ) x^{3} \]
✓ Solution by Mathematica
Time used: 60.209 (sec). Leaf size: 1021
DSolve[(x^3-y[x]^4)y'[x]==3 x^2 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}-\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}-\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}} y(x)\to \frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}+\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}-\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}} y(x)\to -\frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}-\frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}+\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}} y(x)\to \frac {1}{2} \sqrt {-\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}-\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}+\frac {6 c_1}{\sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}}}}-\frac {1}{2} \sqrt {\frac {\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^3}{\sqrt [3]{9 c_1{}^2-\sqrt {-256 x^9+81 c_1{}^4}}}} \end{align*}