Internal problem ID [15516]
Internal file name [OUTPUT/15517_Friday_May_10_2024_05_47_32_PM_27558722/index.tex]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 20. The method of elimination.
Exercises page 212
Problem number: 786.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown" Unable to solve or complete the solution.
Unable to parse ODE.
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 19
dsolve([diff(diff(x(t),t),t) = x(t)^2+y(t), diff(y(t),t) = -2*x(t)*diff(x(t),t)+x(t), x(0) = 1, D(x)(0) = 1, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \\ y \left (t \right ) &= -{\mathrm e}^{2 t}+{\mathrm e}^{t} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]==x[t]^2+y[t],y'[t]==-2*x[t]*x'[t]+x[t]},{x[0]==1,x'[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved