76.3.18 problem 18

Internal problem ID [17389]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 10:04:13 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=y_{0} \end{align*}

✗ Solution by Maple

dsolve([diff(y(t),t)=t^2/(y(t)*(1+t^3)),y(0) = y__0],y(t), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 47

DSolve[{D[y[t],t]==t^2/(y[t]*(1+t^3)),{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt {\frac {2}{3} \log \left (t^3+1\right )+\text {y0}^2} \\ y(t)\to \sqrt {\frac {2}{3} \log \left (t^3+1\right )+\text {y0}^2} \\ \end{align*}