Internal problem ID [12661]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}+4 y=2} \] With initial conditions \begin {align*} [y \left (3\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve([diff(y(t),t)=y(t)^2-4*y(t)+2,y(3) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 2-\sqrt {2}\, \tanh \left (\frac {\left (-6+\sqrt {2}\, \operatorname {arctanh}\left (\frac {\sqrt {2}}{2}\right )+2 t \right ) \sqrt {2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 69
DSolve[{y'[t]==y[t]^2-4*y[t]+2,{y[3]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sqrt {2} \left (e^{2 \sqrt {2} t}+e^{6 \sqrt {2}}\right )}{\left (1+\sqrt {2}\right ) e^{2 \sqrt {2} t}+\left (\sqrt {2}-1\right ) e^{6 \sqrt {2}}} \]