Internal problem ID [3410]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 671.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 931
dsolve(x*(3+5*x-12*x*y(x)^2+4*x^2*y(x))*diff(y(x),x)+(3+10*x-8*x*y(x)^2+6*x^2*y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}{12 x}+\frac {x^{3}+15 x +9}{3 \left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}+\frac {x}{6} \\ y \relax (x ) = -\frac {\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}{24 x}-\frac {x^{3}+15 x +9}{6 \left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}+\frac {x}{6}-\frac {i \sqrt {3}\, \left (\frac {\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}{12 x}-\frac {x^{3}+15 x +9}{3 \left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}\right )}{2} \\ y \relax (x ) = -\frac {\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}{24 x}-\frac {x^{3}+15 x +9}{6 \left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}+\frac {x}{6}+\frac {i \sqrt {3}\, \left (\frac {\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}{12 x}-\frac {x^{3}+15 x +9}{3 \left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {-25 x^{6}+8 x^{5} c_{1}-30 x^{5}-509 x^{4}+180 x^{3} c_{1}-900 x^{3}+108 c_{1} x^{2}-540 x^{2}+108 c_{1}^{2}-108 x}+108 x^{2}+216 c_{1}\right ) x \right )^{\frac {1}{3}}}\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 47.452 (sec). Leaf size: 621
DSolve[x(3+5 x-12 x y[x]^2+4 x^2 y[x])y'[x]+(3+10 x-8 x y[x]^2+6 x^2 y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\left (x^3+15 x+9\right ) x}{3\ 2^{2/3} \sqrt [3]{54 c_1 x^4-\left (\left (2 x^3+45 x+27\right ) x^6\right )+3 \sqrt {3} \sqrt {x^8 \left (-(5 x+3)^2 \left (x^3+20 x+12\right ) x-4 c_1 \left (2 x^3+45 x+27\right ) x^2+108 c_1{}^2\right )}}}-\frac {\sqrt [3]{-8 x^9-180 x^7-108 x^6+216 c_1 x^4+4 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (x^6 \left (2 x^3+45 x+27\right )-54 c_1 x^4\right ){}^2}}}{12 x^2}+\frac {x}{6} \\ y(x)\to \frac {\left (1+i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{54 c_1 x^4-\left (\left (2 x^3+45 x+27\right ) x^6\right )+3 \sqrt {3} \sqrt {x^8 \left (-(5 x+3)^2 \left (x^3+20 x+12\right ) x-4 c_1 \left (2 x^3+45 x+27\right ) x^2+108 c_1{}^2\right )}}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-8 x^9-180 x^7-108 x^6+216 c_1 x^4+4 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (x^6 \left (2 x^3+45 x+27\right )-54 c_1 x^4\right ){}^2}}}{24 x^2}+\frac {x}{6} \\ y(x)\to \frac {\left (1-i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{54 c_1 x^4-\left (\left (2 x^3+45 x+27\right ) x^6\right )+3 \sqrt {3} \sqrt {x^8 \left (-(5 x+3)^2 \left (x^3+20 x+12\right ) x-4 c_1 \left (2 x^3+45 x+27\right ) x^2+108 c_1{}^2\right )}}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-8 x^9-180 x^7-108 x^6+216 c_1 x^4+4 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (x^6 \left (2 x^3+45 x+27\right )-54 c_1 x^4\right ){}^2}}}{24 x^2}+\frac {x}{6} \\ \end{align*}