Internal problem ID [598]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-3 y x^{2}-y^{2}}{2 x^{3}+3 y x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2] \end {align*}
✓ Solution by Maple
Time used: 1.443 (sec). Leaf size: 111
dsolve([diff(y(x),x) = (-3*x^2*y(x)-y(x)^2)/(2*x^3+3*x*y(x)),y(1) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (i \sqrt {3}-1\right ) \left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )^{\frac {1}{3}}-\frac {\left (i x^{3} \sqrt {3}+x^{3}+2 \left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )^{\frac {1}{3}}\right ) x^{3}}{\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )^{\frac {1}{3}}}}{6 x} \]
✓ Solution by Mathematica
Time used: 16.925 (sec). Leaf size: 116
DSolve[{y'[x]== (-3*x^2*y[x]-y[x]^2)/(2*x^3+3*x*y[x]),y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \left (2 i x^3+\left (\sqrt {3}+i\right ) \sqrt [3]{6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}-x^2 \left (x^7+54\right )}-\frac {\left (\sqrt {3}-i\right ) x^6}{\sqrt [3]{6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}-x^2 \left (x^7+54\right )}}\right )}{6 x} \\ \end{align*}