Internal problem ID [12944]
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: 7.
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 ) = 2] \end {align*}
✓ Solution by Maple
Time used: 4.344 (sec). Leaf size: 147
dsolve([diff(y(t),t)=y(t)*(y(t)-1)*(y(t)-3),y(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (16 \,{\mathrm e}^{6 t}+9\right ) \left (1+8 \,{\mathrm e}^{6 t}+4 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}\right )^{\frac {2}{3}}+\left (24 \,{\mathrm e}^{6 t}+12 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}+9\right ) \left (1+8 \,{\mathrm e}^{6 t}+4 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}\right )^{\frac {1}{3}}+48 \,{\mathrm e}^{6 t}+24 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}+9}{\left (16 \,{\mathrm e}^{6 t}+3\right ) \left (1+8 \,{\mathrm e}^{6 t}+4 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}\right )^{\frac {2}{3}}+\left (8 \,{\mathrm e}^{6 t}+4 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}+3\right ) \left (1+8 \,{\mathrm e}^{6 t}+4 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}\right )^{\frac {1}{3}}+16 \,{\mathrm e}^{6 t}+8 \sqrt {{\mathrm e}^{6 t}+4 \,{\mathrm e}^{12 t}}+3} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 105
DSolve[{y'[t]==y[t]*(y[t]-1)*(y[t]-3),{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sqrt [3]{2 \sqrt {e^{6 t} \left (4 e^{6 t}+1\right )^3}+8 e^{6 t}+16 e^{12 t}+1}}{4 e^{6 t}+1}+\frac {1}{\sqrt [3]{2 \sqrt {e^{6 t} \left (4 e^{6 t}+1\right )^3}+8 e^{6 t}+16 e^{12 t}+1}}+1 \]