Internal problem ID [2074]
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: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 86
dsolve([(-2*x^2-3*x*y(x))*diff(y(x),x)+y(x)^2=0,y(1) = 1],y(x), singsol=all)
\[ y = \frac {\left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{\frac {2}{3}}-\left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{\frac {1}{3}} x +x^{2}}{3 \left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 60.281 (sec). Leaf size: 77
DSolve[{(-2*x^2-3*x*y[x])*y'[x]+y[x]^2==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (\frac {x^2}{\sqrt [3]{-x^3+3 \sqrt {81 x^2-6 x^4}+27 x}}+\sqrt [3]{-x^3+3 \sqrt {81 x^2-6 x^4}+27 x}-x\right ) \]