76.1.30 problem 30

Internal problem ID [17329]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 10:01:14 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 x^{2}}{2 y^{2}-6} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.124 (sec). Leaf size: 67

dsolve([diff(y(x),x)=2*x^2/(2*y(x)^2-6),y(1) = 0],y(x), singsol=all)
 

\[ y = -\frac {\left (1+i \sqrt {3}\right ) \left (-4+4 x^{3}+4 \sqrt {x^{6}-2 x^{3}-107}\right )^{{2}/{3}}-12 i \sqrt {3}+12}{4 \left (-4+4 x^{3}+4 \sqrt {x^{6}-2 x^{3}-107}\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 2.594 (sec). Leaf size: 115

DSolve[{D[y[x],x]==2*x^2/(2*y[x]^2-6),{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-i \sqrt [3]{2} \sqrt {3} \left (x^3+\sqrt {x^6-2 x^3-107}-1\right )^{2/3}-\sqrt [3]{2} \left (x^3+\sqrt {x^6-2 x^3-107}-1\right )^{2/3}+6 i \sqrt {3}-6}{2\ 2^{2/3} \sqrt [3]{x^3+\sqrt {x^6-2 x^3-107}-1}} \]