10.2.21 problem 21

Internal problem ID [1149]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 21
Date solved : Monday, January 27, 2025 at 04:36:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}+1}{-6 y+3 y^{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.116 (sec). Leaf size: 107

dsolve([diff(y(x),x) = (3*x^2+1)/(-6*y(x)+3*y(x)^2),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.061 (sec). Leaf size: 158

DSolve[{D[y[x],x] == (3*x^2+1)/(-6*y[x]+3*y[x]^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

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