Internal problem ID [482]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{2}-1}{3+2 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 45
dsolve(diff(y(x),x) = (3*x^2-1)/(3+2*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {3}{2}-\frac {\sqrt {4 x^{3}+4 c_{1}-4 x +9}}{2} \\ y \relax (x ) = -\frac {3}{2}+\frac {\sqrt {4 x^{3}+4 c_{1}-4 x +9}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 59
DSolve[y'[x] == (3*x^2-1)/(3+2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-3-\sqrt {4 x^3-4 x+9+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-3+\sqrt {4 x^3-4 x+9+4 c_1}\right ) \\ \end{align*}