10.3.12 problem 16

Internal problem ID [1177]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:39:27 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(diff(y(t),t) = t^2/(t^3+1)/y(t),y(t), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_1}}{3} \\ y &= \frac {\sqrt {6 \ln \left (t^{3}+1\right )+9 c_1}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 56

DSolve[D[y[t],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*}