Internal problem ID [487]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1-2 x \right ) y^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = -{\frac {1}{6}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.085 (sec). Leaf size: 14
dsolve([diff(y(x),x) = (1-2*x)*y(x)^2,y(0) = -1/6],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{x^{2}-x -6} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 15
DSolve[{y'[x] == (1-2*x)*y[x]^2,y[0]==-1/6},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2-x-6} \\ \end{align*}