Internal problem ID [3918]
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]
\[ \boxed {x \left (3+5 x -12 y^{2} x +4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 y^{2} x +6 x^{2} y\right ) y=0} \]
✓ 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 \left (x \right ) = \frac {{\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{2}-108 x}+108 x^{2}+216 c_{1} \right ) x \right )}^{\frac {1}{3}}}+\frac {x}{6} y \left (x \right ) = -\frac {{\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{2}-108 x}+108 x^{2}+216 c_{1} \right ) x \right )}^{\frac {1}{3}}}\right )}{2} y \left (x \right ) = -\frac {{\left (\left (8 x^{5}+180 x^{3}+12 \sqrt {3}\, \sqrt {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{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 {8 c_{1} x^{5}-25 x^{6}-30 x^{5}+180 c_{1} x^{3}-509 x^{4}+108 c_{1} x^{2}-900 x^{3}+108 c_{1}^{2}-540 x^{2}-108 x}+108 x^{2}+216 c_{1} \right ) x \right )}^{\frac {1}{3}}}\right )}{2} \end{align*}
✓ Solution by Mathematica
Time used: 60.181 (sec). Leaf size: 660
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 {\sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{12 \sqrt [3]{2} x^2}-\frac {\left (x^3+15 x+9\right ) x}{3\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6} y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{24 \sqrt [3]{2} x^2}+\frac {\left (1+i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6} y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^9-360 x^7-216 x^6+432 c_1 x^4+8 \sqrt {-4 x^9 \left (x^3+15 x+9\right )^3+\left (2 x^9+45 x^7+27 x^6-54 c_1 x^4\right ){}^2}}}{24 \sqrt [3]{2} x^2}+\frac {\left (1-i \sqrt {3}\right ) \left (x^3+15 x+9\right ) x}{6\ 2^{2/3} \sqrt [3]{-2 x^9-45 x^7-27 x^6+54 c_1 x^4+3 \sqrt {3} \sqrt {-x^8 \left (25 x^6+(30+8 c_1) x^5+509 x^4+180 (5+c_1) x^3+108 (5+c_1) x^2+108 x-108 c_1{}^2\right )}}}+\frac {x}{6} \end{align*}