Internal problem ID [11394]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-2 t x^{2}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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: 0.183 (sec). Leaf size: 14
DSolve[{x'[t]==2*t*x[t]^2,{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{1-t^2} \]