10.6.31 problem 31

Internal problem ID [1248]
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
Date solved : Monday, January 27, 2025 at 04:47:45 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 1.260 (sec). Leaf size: 109

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)
 

\[ y = \frac {\left (i \sqrt {3}-1\right ) {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{2}/{3}}-x^{3} \left (i \sqrt {3}\, x^{3}+x^{3}+2 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{1}/{3}}\right )}{6 {\left (-\left (x^{7}-6 \sqrt {3}\, \sqrt {x^{7}+27}+54\right ) x^{2}\right )}^{{1}/{3}} x} \]

✓ Solution by Mathematica

Time used: 44.132 (sec). Leaf size: 136

DSolve[{D[y[x],x]== (-3*x^2*y[x]-y[x]^2)/(2*x^3+3*x*y[x]),y[1]==-2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {i \left (\left (\sqrt {3}+i\right ) x^3-\left (\sqrt {3}-i\right ) x^3+\left (\sqrt {3}+i\right ) \sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}-\frac {\left (\sqrt {3}-i\right ) x^6}{\sqrt [3]{-x^9-54 x^2+6 \sqrt {3} \sqrt {x^4 \left (x^7+27\right )}}}\right )}{6 x} \]