Internal problem ID [501]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 y^{2}-x y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.138 (sec). Leaf size: 16
dsolve([diff(y(x),x) = 2*y(x)^2+x*y(x)^2,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {2}{x^{2}+4 x -2} \]
✓ Solution by Mathematica
Time used: 0.133 (sec). Leaf size: 16
DSolve[{y'[x] == 2*y[x]^2+x*y[x]^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{x (x+4)-2} \\ \end{align*}