72.5.30 problem 26

Internal problem ID [14716]
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 : 26
Date solved : Tuesday, January 28, 2025 at 07:12:29 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.164 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 62

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

\[ y(t)\to \frac {\left (4 \sqrt {2}-6\right ) e^{2 \sqrt {2} t}+6+4 \sqrt {2}}{\left (\sqrt {2}-2\right ) e^{2 \sqrt {2} t}+2+\sqrt {2}} \]