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`]]
\[ \boxed {y^{\prime }-\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 1.266 (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)
\[ y \left (x \right ) = \frac {\left (i \sqrt {3}-1\right ) {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{\frac {2}{3}}-x^{3} \left (i \sqrt {3}\, x^{3}+x^{3}+2 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{\frac {1}{3}}\right )}{6 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{\frac {1}{3}} x} \]
✓ Solution by Mathematica
Time used: 40.923 (sec). Leaf size: 136
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]
\[ y(x)\to \frac {i \left (\left (\sqrt {3}+i\right ) x^3-\left (\sqrt {3}-i\right ) x^3+\left (\sqrt {3}+i\right ) \sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}-\frac {\left (\sqrt {3}-i\right ) x^6}{\sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}}\right )}{6 x} \]