72.1.32 problem 35

Internal problem ID [14632]
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
Date solved : Tuesday, January 28, 2025 at 06:45:24 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 14

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

\[ y = \tan \left (\frac {t^{2}}{2}+\frac {\pi }{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 17

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

\[ y(t)\to \tan \left (\frac {1}{4} \left (2 t^2+\pi \right )\right ) \]