74.4.31 problem 31

Internal problem ID [15924]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 08:22:53 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(diff(y(t),t)=t^2*y(t)^2+y(t)^2-t^2-1,y(t), singsol=all)
 

\[ y = -\tanh \left (\frac {1}{3} t^{3}+c_{1} +t \right ) \]

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 49

DSolve[D[y[t],t]==t^2*y[t]^2+y[t]^2-t^2-1,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+1)}dK[1]\&\right ]\left [\frac {t^3}{3}+t+c_1\right ] \\ y(t)\to -1 \\ y(t)\to 1 \\ \end{align*}