Internal problem ID [3440]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 702.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {\left (2-10 y^{3} x^{2}+3 y^{2}\right ) y^{\prime }-x \left (1+5 y^{4}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve((2-10*x^2*y(x)^3+3*y(x)^2)*diff(y(x),x) = x*(1+5*y(x)^4),y(x), singsol=all)
\[ \frac {\left (-5 y \relax (x )^{4}-1\right ) x^{2}}{2}+y \relax (x )^{3}+2 y \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 2097
DSolve[(2-10 x^2 y[x]^3+3 y[x]^2)y'[x]==x(1+5 y[x]^4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {3} x^2 \sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}+\sqrt {3} x^2 \sqrt {-\frac {-6 x^2+5 \sqrt [3]{6} x^4 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^4 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}}}{x^6}}-3}{30 x^2} \\ y(x)\to \frac {-\sqrt {3} x^2 \sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}+\sqrt {3} x^2 \sqrt {-\frac {-6 x^2+5 \sqrt [3]{6} x^4 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^4 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}}}{x^6}}+3}{30 x^2} \\ y(x)\to \frac {\sqrt {3} x^2 \sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}-\sqrt {3} x^2 \sqrt {\frac {6 x^2-5 \sqrt [3]{6} x^4 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}-\frac {10\ 6^{2/3} x^4 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}}}{x^6}}+3}{30 x^2} \\ y(x)\to \frac {\sqrt {3} x^2 \sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}+\sqrt {3} x^2 \sqrt {\frac {6 x^2-5 \sqrt [3]{6} x^4 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}-\frac {10\ 6^{2/3} x^4 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+\frac {6 \sqrt {3} \left (100 x^4+1\right )}{\sqrt {\frac {5 \sqrt [3]{6} x^2 \sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}+\frac {10\ 6^{2/3} x^2 \left (5 x^4-10 c_1 x^2-2\right )}{\sqrt [3]{189 x^2+\sqrt {3} \sqrt {27 \left (21 x^2-2 c_1\right ){}^2-16 \left (5 x^4-10 c_1 x^2-2\right ){}^3}-18 c_1}}+3}{x^4}}}}{x^6}}+3}{30 x^2} \\ \end{align*}