72.1.29 problem 32

Internal problem ID [14629]
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 : 32
Date solved : Tuesday, January 28, 2025 at 06:45:11 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 16

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

\[ y = -\frac {2}{t^{2}+4 t -2} \]

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 17

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

\[ y(t)\to -\frac {2}{t^2+4 t-2} \]