63.4.17 problem 7

Internal problem ID [13060]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 04:50:46 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=2 t x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 13

dsolve([diff(x(t),t)=2*t*x(t)^2,x(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {1}{t^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 14

DSolve[{D[x[t],t]==2*t*x[t]^2,{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{1-t^2} \]