Internal problem ID [12625]
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 1.5 page 71
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y \left (y-1\right ) \left (y-3\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 1.125 (sec). Leaf size: 133
dsolve([diff(y(t),t)=y(t)*(y(t)-1)*(y(t)-3),y(0) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (2 \,{\mathrm e}^{6 t}-4\right ) \left (1-{\mathrm e}^{6 t}+\sqrt {{\mathrm e}^{6 t} \left ({\mathrm e}^{6 t}-2\right )}\right )^{\frac {2}{3}}+\left (\left (i \sqrt {3}-1\right ) \left (1-{\mathrm e}^{6 t}+\sqrt {{\mathrm e}^{6 t} \left ({\mathrm e}^{6 t}-2\right )}\right )^{\frac {1}{3}}-i \sqrt {3}-1\right ) \left ({\mathrm e}^{6 t}-\sqrt {{\mathrm e}^{6 t} \left ({\mathrm e}^{6 t}-2\right )}-2\right )}{\left (1-{\mathrm e}^{6 t}+\sqrt {{\mathrm e}^{6 t} \left ({\mathrm e}^{6 t}-2\right )}\right )^{\frac {2}{3}} \left (2 \,{\mathrm e}^{6 t}-4\right )} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 104
DSolve[{y'[t]==y[t]*(y[t]-1)*(y[t]-3),{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sqrt [3]{2 \sqrt {e^{6 t} \left (e^{6 t}-2\right )^3}+8 e^{6 t}-2 e^{12 t}-8}}{e^{6 t}-2}-\frac {2^{2/3}}{\sqrt [3]{\sqrt {e^{6 t} \left (e^{6 t}-2\right )^3}+4 e^{6 t}-e^{12 t}-4}}+1 \]