15.8.42 problem 44

Internal problem ID [3045]
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
Date solved : Monday, January 27, 2025 at 07:11:28 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (-2 x^{2}-3 y x \right ) y^{\prime }+y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.569 (sec). Leaf size: 100

dsolve([(-2*x^2-3*x*y(x))*diff(y(x),x)+y(x)^2=0,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{{2}/{3}}-x \left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{{1}/{3}}+x^{2}}{3 \left (-x^{3}+3 \sqrt {-2 x^{4}+27 x^{2}}\, \sqrt {3}+27 x \right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 60.309 (sec). Leaf size: 77

DSolve[{(-2*x^2-3*x*y[x])*D[y[x],x]+y[x]^2==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (\frac {x^2}{\sqrt [3]{-x^3+3 \sqrt {81 x^2-6 x^4}+27 x}}+\sqrt [3]{-x^3+3 \sqrt {81 x^2-6 x^4}+27 x}-x\right ) \]