Internal problem ID [3935]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 688.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {\left (3 x^{3}+6 x^{2} y-3 y^{2} x +20 y^{3}\right ) y^{\prime }+9 x^{2} y+6 y^{2} x -y^{3}=-4 x^{3}} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 50
dsolve((3*x^3+6*x^2*y(x)-3*x*y(x)^2+20*y(x)^3)*diff(y(x),x)+4*x^3+9*x^2*y(x)+6*x*y(x)^2-y(x)^3 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (c_{1}^{4} x^{4}+3 \textit {\_Z} \,c_{1}^{3} x^{3}+3 \textit {\_Z}^{2} c_{1}^{2} x^{2}-\textit {\_Z}^{3} c_{1} x +5 \textit {\_Z}^{4}-1\right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 60.176 (sec). Leaf size: 2201
DSolve[(3 x^3+6 x^2 y[x]-3 x y[x]^2+20 y[x]^3)y'[x]+4 x^3+9 x^2 y[x]+6 x y[x]^2-y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}-\frac {1}{2} \sqrt {-\frac {39 x^2}{50}-\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (-13 x^4+10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}-\frac {659 x^3}{500 \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}}}+\frac {x}{20} \\ y(x)\to \frac {1}{2} \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}+\frac {1}{2} \sqrt {-\frac {39 x^2}{50}-\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (-13 x^4+10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}-\frac {659 x^3}{500 \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}}}+\frac {x}{20} \\ y(x)\to -\frac {1}{2} \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}-\frac {1}{2} \sqrt {-\frac {39 x^2}{50}-\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (-13 x^4+10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}+\frac {659 x^3}{500 \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}}}+\frac {x}{20} \\ y(x)\to -\frac {1}{2} \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}+\frac {1}{2} \sqrt {-\frac {39 x^2}{50}-\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (-13 x^4+10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}+\frac {659 x^3}{500 \sqrt {-\frac {39 x^2}{100}+\frac {\sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}{5 \sqrt [3]{2} 3^{2/3}}+\frac {2 \sqrt [3]{\frac {2}{3}} \left (13 x^4-10 e^{c_1}\right )}{5 \sqrt [3]{99 x^6+351 e^{c_1} x^2+\sqrt {3} \sqrt {-67037 x^{12}+185406 e^{c_1} x^8-83733 e^{2 c_1} x^4+32000 e^{3 c_1}}}}}}}+\frac {x}{20} \\ \end{align*}