Internal problem ID [12942]
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: 5.
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 ) = 4] \end {align*}
✓ Solution by Maple
Time used: 1.828 (sec). Leaf size: 133
dsolve([diff(y(t),t)=y(t)*(y(t)-1)*(y(t)-3),y(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {48 \left (\frac {{\mathrm e}^{6 t}}{3}-\frac {9}{16}\right ) \left (27-32 \,{\mathrm e}^{6 t}+8 \sqrt {16 \,{\mathrm e}^{12 t}-27 \,{\mathrm e}^{6 t}}\right )^{\frac {2}{3}}+48 \left (\left (27-32 \,{\mathrm e}^{6 t}+8 \sqrt {16 \,{\mathrm e}^{12 t}-27 \,{\mathrm e}^{6 t}}\right )^{\frac {1}{3}}+3\right ) \left ({\mathrm e}^{6 t}-\frac {\sqrt {16 \,{\mathrm e}^{12 t}-27 \,{\mathrm e}^{6 t}}}{4}-\frac {27}{16}\right )}{\left (27-32 \,{\mathrm e}^{6 t}+8 \sqrt {16 \,{\mathrm e}^{12 t}-27 \,{\mathrm e}^{6 t}}\right )^{\frac {2}{3}} \left (16 \,{\mathrm e}^{6 t}-27\right )} \]
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 132
DSolve[{y'[t]==y[t]*(y[t]-1)*(y[t]-3),{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3 i \left (\sqrt {3}+i\right ) \sqrt [3]{4 \sqrt {e^{6 t} \left (16 e^{6 t}-27\right )^3}+864 e^{6 t}-256 e^{12 t}-729}}{32 e^{6 t}-54}+\frac {9 \left (1+i \sqrt {3}\right )}{2 \sqrt [3]{4 \sqrt {e^{6 t} \left (16 e^{6 t}-27\right )^3}+864 e^{6 t}-256 e^{12 t}-729}}+1 \]