Internal problem ID [499]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{2}+1}{-6 y+3 y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.107 (sec). Leaf size: 109
dsolve([diff(y(x),x) = (3*x^2+1)/(-6*y(x)+3*y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (1+i \sqrt {3}\right ) \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{\frac {2}{3}}-4 i \sqrt {3}-4 \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{\frac {1}{3}}+4}{4 \left (4 x^{3}+4 x +4 \sqrt {x^{6}+2 x^{4}+x^{2}-4}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 3.942 (sec). Leaf size: 110
DSolve[{y'[x] == (3*x^2+1)/(-6*y[x]+3*y[x]^2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-i 2^{2/3} \sqrt {3} \sqrt [3]{x^3+\sqrt {\left (x^3+x\right )^2-4}+x}-2^{2/3} \sqrt [3]{x^3+\sqrt {\left (x^3+x\right )^2-4}+x}+\frac {4 (-1)^{2/3} \sqrt [3]{2}}{\sqrt [3]{x^3+\sqrt {\left (x^3+x\right )^2-4}+x}}+4\right ) \\ \end{align*}