Internal problem ID [500]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{2}}{-4+3 y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 73
dsolve([diff(y(x),x) = 3*x^2/(-4+3*y(x)^2),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (1+i \sqrt {3}\right ) \left (-108+108 x^{3}+12 \sqrt {81 x^{6}-162 x^{3}-687}\right )^{\frac {2}{3}}-48 i \sqrt {3}+48}{12 \left (-108+108 x^{3}+12 \sqrt {81 x^{6}-162 x^{3}-687}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 9.504 (sec). Leaf size: 137
DSolve[{y'[x]== 3*x^2/(-4+3*y[x]^2),y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-i \sqrt [3]{2} 3^{2/3} \left (9 x^3+\sqrt {81 x^3 \left (x^3-2\right )-687}-9\right )^{2/3}-\sqrt [3]{2} \sqrt [6]{3} \left (9 x^3+\sqrt {81 x^3 \left (x^3-2\right )-687}-9\right )^{2/3}-8 \sqrt {3}+24 i}{2\ 2^{2/3} 3^{5/6} \sqrt [3]{9 x^3+\sqrt {81 x^3 \left (x^3-2\right )-687}-9}} \\ \end{align*}