72.5.28 problem 24

Internal problem ID [14714]
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 1.6 page 89
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 07:12:25 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-4 y+2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.145 (sec). Leaf size: 24

dsolve([diff(y(t),t)=y(t)^2-4*y(t)+2,y(0) = -2],y(t), singsol=all)
 

\[ y = 2-\sqrt {2}\, \tanh \left (\operatorname {arctanh}\left (2 \sqrt {2}\right )+\sqrt {2}\, t \right ) \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 59

DSolve[{D[y[t],t]==y[t]^2-4*y[t]+2,{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {2 \left (\left (\sqrt {2}-3\right ) e^{2 \sqrt {2} t}+3+\sqrt {2}\right )}{\left (4+\sqrt {2}\right ) e^{2 \sqrt {2} t}-4+\sqrt {2}} \]