Internal problem ID [480]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}}{\left (x^{3}+1\right ) y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 39
dsolve(diff(y(x),x) = x^2/(x^3+1)/y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_{1}}}{3} \\ y \relax (x ) = \frac {\sqrt {6 \ln \left (x^{3}+1\right )+9 c_{1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 56
DSolve[y'[x] == x^2/(x^3+1)/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ y(x)\to \sqrt {\frac {2}{3}} \sqrt {\log \left (x^3+1\right )+3 c_1} \\ \end{align*}