76.1.29 problem 29

Internal problem ID [17328]
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 : 29
Date solved : Tuesday, January 28, 2025 at 10:01:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{12 y^{2}-12 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.131 (sec). Leaf size: 72

dsolve([diff(y(x),x)=(1+3*x^2)/(12*y(x)^2-12*y(x)),y(0) = 2],y(x), singsol=all)
 

\[ y = \frac {\left (9+x^{3}+x +\sqrt {x^{6}+2 x^{4}+18 x^{3}+x^{2}+18 x +80}\right )^{{1}/{3}}}{2}+\frac {1}{2 \left (9+x^{3}+x +\sqrt {x^{6}+2 x^{4}+18 x^{3}+x^{2}+18 x +80}\right )^{{1}/{3}}}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 4.034 (sec). Leaf size: 81

DSolve[{D[y[x],x]==(1+3*x^2)/(12*y[x]^2-12*y[x]),{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt [3]{x^3+\sqrt {x^6+2 x^4+18 x^3+x^2+18 x+80}+x+9}+\frac {1}{\sqrt [3]{x^3+\sqrt {x^6+2 x^4+18 x^3+x^2+18 x+80}+x+9}}+1\right ) \]