Internal problem ID [12896]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.2. page
33
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (1+y^{2}\right ) t=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
dsolve([diff(y(t),t)=(y(t)^2+1)*t,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \tan \left (\frac {t^{2}}{2}+\frac {\pi }{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.29 (sec). Leaf size: 17
DSolve[{y'[t]==(y[t]^2+1)*t,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \tan \left (\frac {1}{4} \left (2 t^2+\pi \right )\right ) \]