72.5.31 problem 27

Internal problem ID [14717]
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 : 27
Date solved : Tuesday, January 28, 2025 at 07:12:31 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.158 (sec). Leaf size: 32

dsolve([diff(y(t),t)=y(t)^2-4*y(t)+2,y(3) = 1],y(t), singsol=all)
 

\[ y = 2-\sqrt {2}\, \tanh \left (\frac {\left (\sqrt {2}\, \operatorname {arctanh}\left (\frac {\sqrt {2}}{2}\right )+2 t -6\right ) \sqrt {2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 69

DSolve[{D[y[t],t]==y[t]^2-4*y[t]+2,{y[3]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\sqrt {2} \left (e^{2 \sqrt {2} t}+e^{6 \sqrt {2}}\right )}{\left (1+\sqrt {2}\right ) e^{2 \sqrt {2} t}+\left (\sqrt {2}-1\right ) e^{6 \sqrt {2}}} \]