Internal problem ID [491]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x}{y+x^{2} y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([diff(y(x),x) = 2*x/(y(x)+x^2*y(x)),y(0) = -2],y(x), singsol=all)
\[ y \relax (x ) = -\sqrt {2 \ln \left (x^{2}+1\right )+4} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 24
DSolve[{y'[x] == 2*x/(y[x]+x^2*y[x]),y[0]==-2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {\log \left (x^2+1\right )+2} \\ \end{align*}