76.10.11 problem 11

Internal problem ID [17533]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 08:27:41 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )^{2} y \left (t \right )-3 x \left (t \right )^{2}-4 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right ) y \left (t \right )^{2}+6 x \left (t \right ) y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.421 (sec). Leaf size: 102

dsolve([diff(x(t),t)=2*x(t)^2*y(t)-3*x(t)^2-4*y(t),diff(y(t),t)=-2*x(t)*y(t)^2+6*x(t)*y(t)],singsol=all)
 

\begin{align*} \left \{x \left (t \right ) &= \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{\sqrt {9 \textit {\_a}^{4}+c_{1} \textit {\_a}^{2}-18 \textit {\_a}^{2}-2 c_{1} +36}}d \textit {\_a} +t +c_{2} \right ), x \left (t \right ) = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}-\frac {1}{\sqrt {9 \textit {\_a}^{4}+c_{1} \textit {\_a}^{2}-18 \textit {\_a}^{2}-2 c_{1} +36}}d \textit {\_a} +t +c_{2} \right )\right \} \\ \left \{y \left (t \right ) &= \frac {-3 x \left (t \right )^{2}-\frac {d}{d t}x \left (t \right )}{-2 x \left (t \right )^{2}+4}\right \} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.602 (sec). Leaf size: 2113

DSolve[{D[x[t],t]==2*x[t]^2*y[t]-3*x[t]^2-4*y[t],D[y[t],t]==-2*x[t]*y[t]^2+6*x[t]*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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