Internal problem ID [6377]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 85.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-2 y \left (x \sqrt {y}-1\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 9
dsolve([diff(y(x),x)= 2*y(x)*(x*sqrt(y(x)) - 1),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{\left (x +1\right )^{2}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y'[x]==2*y[x]*(x*sqrt[y[x]-1]),{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
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