Internal problem ID [6102]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations.
Page 250
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=y_{2} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=6 y_{1} \left (x \right )+y_{2} \left (x \right ) \end {align*}
With initial conditions \[ [y_{1} \left (0\right ) = 1, y_{2} \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve([diff(y__1(x),x) = y__2(x), diff(y__2(x),x) = 6*y__1(x)+y__2(x), y__1(0) = 1, y__2(0) = -1], singsol=all)
\begin{align*} y_{1} \left (x \right ) &= \frac {4 \,{\mathrm e}^{-2 x}}{5}+\frac {{\mathrm e}^{3 x}}{5} \\ y_{2} \left (x \right ) &= -\frac {8 \,{\mathrm e}^{-2 x}}{5}+\frac {3 \,{\mathrm e}^{3 x}}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 42
DSolve[{y1'[x]==y2[x],y2'[x]==6*y1[x]+y2[x]},{y1[0]==1,y2[0]==-1},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{5} e^{-2 x} \left (e^{5 x}+4\right ) \\ \text {y2}(x)\to \frac {1}{5} e^{-2 x} \left (3 e^{5 x}-8\right ) \\ \end{align*}