Internal problem ID [2048]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y+\left (3 x -2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((y(x))+(3*x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ x -\frac {y}{2}-\frac {c_{1}}{y^{3}} = 0 \]
✓ Solution by Mathematica
Time used: 60.08 (sec). Leaf size: 1509
DSolve[(y[x])+(3*x-2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}-\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} y(x)\to -\frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}+\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}-\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} y(x)\to \frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}-\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}+\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} y(x)\to \frac {1}{2} \sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}+\frac {1}{2} \sqrt {2 x^2-\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}-\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}+\frac {2 x^3}{\sqrt {x^2+\frac {\sqrt [3]{2} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}{3^{2/3}}+\frac {2\ 2^{2/3} e^{2 c_1}}{\sqrt [3]{3} \sqrt [3]{\sqrt {81 e^{4 c_1} x^4-48 e^{6 c_1}}+9 e^{2 c_1} x^2}}}}}+\frac {x}{2} \end{align*}