Internal problem ID [527]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {t^{2}}{\left (t^{3}+1\right ) y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(t),t) = t^2/(t^3+1)/y(t),y(t), singsol=all)
\begin{align*} y \relax (t ) = -\frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_{1}}}{3} \\ y \relax (t ) = \frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_{1}}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 56
DSolve[y'[t] == t^2/(t^3+1)/y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+3 c_1} \\ y(t)\to \sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+3 c_1} \\ \end{align*}