Internal problem ID [3435]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 697.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 31
dsolve(x*(x^4-2*y(x)^3)*diff(y(x),x)+(2*x^4+y(x)^3)*y(x) = 0,y(x), singsol=all)
\[ \ln \relax (x )-c_{1}+\frac {3 \ln \left (-\frac {y \relax (x ) \left (2 x^{4}-y \relax (x )^{3}\right )}{x^{\frac {16}{3}}}\right )}{10} = 0 \]
✓ Solution by Mathematica
Time used: 60.134 (sec). Leaf size: 1139
DSolve[x(x^4-2 y[x]^3)y'[x]+(2 x^4+y[x]^3)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-\sqrt [6]{2} 3^{2/3} \sqrt {\frac {4 \sqrt [3]{6} c_1 x^2+\left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}-3 \sqrt {-\frac {\sqrt [3]{18 x^8-2 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}{3^{2/3}}-\frac {4\ 2^{2/3} c_1 x^2}{\sqrt [3]{27 x^8-3 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}-\frac {4 \sqrt {3} x^4}{\sqrt {\frac {4\ 6^{2/3} c_1 x^2+\sqrt [3]{6} \left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}}}\right ) \\ y(x)\to \frac {1}{6} \left (3 \sqrt {-\frac {\sqrt [3]{18 x^8-2 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}{3^{2/3}}-\frac {4\ 2^{2/3} c_1 x^2}{\sqrt [3]{27 x^8-3 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}-\frac {4 \sqrt {3} x^4}{\sqrt {\frac {4\ 6^{2/3} c_1 x^2+\sqrt [3]{6} \left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}}}-\sqrt [6]{2} 3^{2/3} \sqrt {\frac {4 \sqrt [3]{6} c_1 x^2+\left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt [6]{2} 3^{2/3} \sqrt {\frac {4 \sqrt [3]{6} c_1 x^2+\left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}-3 \sqrt {-\frac {\sqrt [3]{18 x^8-2 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}{3^{2/3}}-\frac {4\ 2^{2/3} c_1 x^2}{\sqrt [3]{27 x^8-3 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}+\frac {4 \sqrt {3} x^4}{\sqrt {\frac {4\ 6^{2/3} c_1 x^2+\sqrt [3]{6} \left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}}}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt [6]{2} 3^{2/3} \sqrt {\frac {4 \sqrt [3]{6} c_1 x^2+\left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}+3 \sqrt {-\frac {\sqrt [3]{18 x^8-2 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}{3^{2/3}}-\frac {4\ 2^{2/3} c_1 x^2}{\sqrt [3]{27 x^8-3 \sqrt {81 x^{16}-384 c_1{}^3 x^6}}}+\frac {4 \sqrt {3} x^4}{\sqrt {\frac {4\ 6^{2/3} c_1 x^2+\sqrt [3]{6} \left (9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}\right ){}^{2/3}}{\sqrt [3]{9 x^8-\sqrt {81 x^{16}-384 c_1{}^3 x^6}}}}}}\right ) \\ \end{align*}