Internal problem ID [492]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x y^{2}}{\sqrt {x^{2}+1}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 17
dsolve([diff(y(x),x) = x*y(x)^2/(x^2+1)^(1/2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{\sqrt {x^{2}+1}-2} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 20
DSolve[{y'[x] == x*y[x]^2/(x^2+1)^(1/2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2-\sqrt {x^2+1}} \\ \end{align*}