2.17.4 Problems 301 to 400

Problem 301

ODE	\[ \boxed {y^{\prime \prime \prime }+27 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{\left (\frac {3}{2}+\frac {3 i \sqrt {3}}{2}\right ) x} c_{2} +{\mathrm e}^{\left (\frac {3}{2}-\frac {3 i \sqrt {3}}{2}\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {9 x}{2}} \sin \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {9 x}{2}} \cos \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_{1} \right ) {\mathrm e}^{-3 x} \]

Problem 302

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-i \sqrt {3}\, x} c_{3} +{\mathrm e}^{i \sqrt {3}\, x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x}+c_{3} \sin \left (\sqrt {3}\, x \right )+c_{4} \cos \left (\sqrt {3}\, x \right ) \]

Problem 303

ODE	\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{x}+{\mathrm e}^{\left (-2-2 i\right ) x} c_{2} +{\mathrm e}^{\left (-2+2 i\right ) x} c_{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{3 x}+\sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{3} \right ) {\mathrm e}^{-2 x} \]

Problem 304

ODE	\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y=0} \]
program solution	\[ y = c_{1} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{2} +x^{2} {\mathrm e}^{-x} c_{3} +{\mathrm e}^{2 x} c_{4} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (c_{4} x^{2}+c_{3} x +c_{2} \right ) {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{1} \]

Problem 305

ODE	\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 10, y^{\prime \prime }\left (0\right ) = 250] \end {align*}
program solution	\[ y = 2 \,{\mathrm e}^{5 x}-2 \cos \left (10 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \,{\mathrm e}^{5 x}-2 \cos \left (10 x \right ) \]

Problem 306

ODE	\[ \boxed {y^{\prime \prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {{\mathrm e}^{x}}{3}+\frac {{\mathrm e}^{\frac {\left (i \sqrt {3}-1\right ) x}{2}}}{3}+\frac {{\mathrm e}^{-\frac {\left (1+i \sqrt {3}\right ) x}{2}}}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{3}+\frac {2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )}{3} \]

Problem 307

ODE	\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = 15] \end {align*}
program solution	\[ y = -\frac {5 \,{\mathrm e}^{-x}}{2}+{\mathrm e}^{2 x}+\frac {3 \cos \left (x \right )}{2}-\frac {9 \sin \left (x \right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = {\mathrm e}^{2 x}-\frac {5 \,{\mathrm e}^{-x}}{2}-\frac {9 \sin \left (x \right )}{2}+\frac {3 \cos \left (x \right )}{2} \]

Problem 308

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x=0} \]
program solution	\[ y = c_{1} +c_{2} \ln \left (x \right )+\frac {c_{3}}{x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} +c_{2} \ln \left (x \right )+\frac {c_{3}}{x^{3}} \]

Problem 309

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+y^{\prime } x=0} \]
program solution	\[ y = c_{2} x^{2}+c_{1} +c_{3} \ln \left (x \right ) x^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} +c_{2} x^{2}+c_{3} x^{2} \ln \left (x \right ) \]

Problem 310

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x=0} \]
program solution	\[ y = c_{1} +c_{2} \ln \left (x \right )+c_{3} \ln \left (x \right )^{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{3} \ln \left (x \right )^{2}+c_{2} \ln \left (x \right )+c_{1} \]

Problem 311

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+y^{\prime } x=0} \]
program solution	\[ y = c_{1} +c_{2} x^{3+\sqrt {3}}+c_{3} x^{3-\sqrt {3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} +c_{2} x^{3+\sqrt {3}}+c_{3} x^{3-\sqrt {3}} \]

Problem 312

ODE	\[ \boxed {x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y=0} \]
program solution	\[ y = \frac {c_{1}}{x}+\frac {c_{2} \ln \left (x \right )}{x}+\frac {c_{3} \ln \left (x \right )^{2}}{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {c_{3} \ln \left (x \right )^{2}+c_{2} \ln \left (x \right )+c_{1}}{x} \]

Problem 313

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{6 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{6 t}}{7}+{\mathrm e}^{-t} c_{1} \\ \end{align*}

Problem 314

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= 3 c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{-2 t}}{2} \\ \end{align*}

Problem 315

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{-t} \\ \end{align*}

Problem 316

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= \frac {2 c_{1} {\mathrm e}^{4 t}}{3}-c_{2} {\mathrm e}^{-t} \\ \end{align*}

Problem 317

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 1] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -\frac {{\mathrm e}^{-t}}{7}+\frac {8 \,{\mathrm e}^{6 t}}{7} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-t}}{7}+\frac {6 \,{\mathrm e}^{6 t}}{7} \\ \end{align*}

Problem 318

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -6 c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{5 t} \\ \end{align*}

Problem 319

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-7 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +\frac {c_{2} {\mathrm e}^{5 t}}{7} \\ \end{align*}

Problem 320

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 0] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= 6 \,{\mathrm e}^{4 t}-5 \,{\mathrm e}^{3 t} \\ x_{2} \left (t \right ) &= -6 \,{\mathrm e}^{4 t}+6 \,{\mathrm e}^{3 t} \\ \end{align*}

Problem 321

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-9 t}+c_{2} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{1} {\mathrm e}^{-9 t}}{2}+c_{2} {\mathrm e}^{t} \\ \end{align*}

Problem 322

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right ) \\ x_{2} \left (t \right ) &= -\frac {2 c_{1} \cos \left (2 t \right )}{5}+\frac {2 c_{2} \sin \left (2 t \right )}{5}+\frac {c_{1} \sin \left (2 t \right )}{5}+\frac {c_{2} \cos \left (2 t \right )}{5} \\ \end{align*}

Problem 323

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 2, x_{2} \left (0\right ) = 3] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -\frac {11 \sin \left (4 t \right )}{4}+2 \cos \left (4 t \right ) \\ x_{2} \left (t \right ) &= 3 \cos \left (4 t \right )+\frac {\sin \left (4 t \right )}{2} \\ \end{align*}

Problem 324

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \\ x_{2} \left (t \right ) &= -\frac {3 c_{1} \cos \left (3 t \right )}{2}+\frac {3 c_{2} \sin \left (3 t \right )}{2}-\frac {3 c_{1} \sin \left (3 t \right )}{2}-\frac {3 c_{2} \cos \left (3 t \right )}{2} \\ \end{align*}

Problem 325

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 4] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -4 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ x_{2} \left (t \right ) &= 4 \,{\mathrm e}^{t} \cos \left (2 t \right ) \\ \end{align*}

Problem 326

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (2 c_{1} \cos \left (2 t \right )+c_{2} \cos \left (2 t \right )+c_{1} \sin \left (2 t \right )-2 c_{2} \sin \left (2 t \right )\right )}{5} \\ \end{align*}

Problem 327

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-9 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right )\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (c_{1} \sin \left (3 t \right )+c_{2} \sin \left (3 t \right )-c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )\right )}{3} \\ \end{align*}

Problem 328

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )\right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{3 t} \left (c_{1} \cos \left (4 t \right )-c_{2} \sin \left (4 t \right )\right ) \\ \end{align*}

Problem 329

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )\right ) \\ x_{2} \left (t \right ) &= -\frac {2 \,{\mathrm e}^{5 t} \left (2 c_{1} \cos \left (4 t \right )-c_{2} \cos \left (4 t \right )-c_{1} \sin \left (4 t \right )-2 c_{2} \sin \left (4 t \right )\right )}{5} \\ \end{align*}

Problem 330

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-50 x_{1} \left (t \right )+20 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=100 x_{1} \left (t \right )-60 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-100 t}+c_{2} {\mathrm e}^{-10 t} \\ x_{2} \left (t \right ) &= -\frac {5 c_{1} {\mathrm e}^{-100 t}}{2}+2 c_{2} {\mathrm e}^{-10 t} \\ \end{align*}

Problem 331

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= -2 c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t}-c_{1} \\ \end{align*}

Problem 332

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} +c_{3} {\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= 2 c_{3} {\mathrm e}^{9 t}+{\mathrm e}^{6 t} c_{1} -\frac {c_{2}}{4} \\ x_{3} \left (t \right ) &= 2 c_{3} {\mathrm e}^{9 t}-{\mathrm e}^{6 t} c_{1} -\frac {c_{2}}{4} \\ \end{align*}

Problem 333

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{6 t} \\ x_{2} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{6 t}+c_{1} {\mathrm e}^{3 t} \\ x_{3} \left (t \right ) &= -2 c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{6 t}-c_{1} {\mathrm e}^{3 t} \\ \end{align*}

Problem 334

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{6 t} c_{1} +c_{2} {\mathrm e}^{9 t}+c_{3} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= -2 \,{\mathrm e}^{6 t} c_{1} +c_{2} {\mathrm e}^{9 t} \\ x_{3} \left (t \right ) &= {\mathrm e}^{6 t} c_{1} +c_{2} {\mathrm e}^{9 t}-c_{3} {\mathrm e}^{2 t} \\ \end{align*}

Problem 335

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-t}}{2}+\frac {c_{3} {\mathrm e}^{t}}{3}+\frac {c_{1}}{3} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{-t}+\frac {2 c_{3} {\mathrm e}^{t}}{3}+\frac {5 c_{1}}{6} \\ \end{align*}

Problem 336

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{3 t}-c_{3} {\mathrm e}^{t}+c_{1} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}-c_{1} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 337

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{3 t}-c_{3} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}-c_{1} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 338

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} \sin \left (2 t \right )+c_{3} \cos \left (2 t \right ) \\ x_{2} \left (t \right ) &= -c_{1} {\mathrm e}^{t}-c_{2} \sin \left (2 t \right )-c_{3} \cos \left (2 t \right )+c_{2} \cos \left (2 t \right )-c_{3} \sin \left (2 t \right ) \\ x_{3} \left (t \right ) &= -c_{2} \cos \left (2 t \right )+c_{3} \sin \left (2 t \right )+c_{2} \sin \left (2 t \right )+c_{3} \cos \left (2 t \right ) \\ \end{align*}

Problem 339

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )+c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right ) \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{2 t} \sin \left (3 t \right )+c_{2} {\mathrm e}^{2 t} \cos \left (3 t \right )-c_{3} {\mathrm e}^{2 t} \cos \left (3 t \right )-c_{3} {\mathrm e}^{2 t} \sin \left (3 t \right )-c_{1} \\ x_{3} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} \sin \left (3 t \right )+\sin \left (3 t \right ) c_{3} -c_{2} \cos \left (3 t \right )+\cos \left (3 t \right ) c_{3} \right ) \\ \end{align*}

Problem 340

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 0, x_{3} \left (0\right ) = 17] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= 4 \,{\mathrm e}^{3 t}+{\mathrm e}^{-t} \sin \left (t \right )-4 \,{\mathrm e}^{-t} \cos \left (t \right ) \\ x_{2} \left (t \right ) &= 9 \,{\mathrm e}^{3 t}-9 \,{\mathrm e}^{-t} \cos \left (t \right )-2 \,{\mathrm e}^{-t} \sin \left (t \right ) \\ x_{3} \left (t \right ) &= 17 \,{\mathrm e}^{-t} \cos \left (t \right ) \\ \end{align*}

Problem 341

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=4 x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{4} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -2 c_{4} {\mathrm e}^{t}+c_{3} {\mathrm e}^{2 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}-3 c_{3} {\mathrm e}^{2 t}+3 c_{4} {\mathrm e}^{t} \\ x_{4} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}-4 c_{2} {\mathrm e}^{3 t}+6 c_{3} {\mathrm e}^{2 t}-4 c_{4} {\mathrm e}^{t} \\ \end{align*}

Problem 342

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+9 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-x_{3} \left (t \right )+8 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= 3 c_{4} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{2 t}-2 c_{4} {\mathrm e}^{t}-c_{2} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= 4 c_{4} {\mathrm e}^{t}+c_{3} {\mathrm e}^{-t} \\ x_{4} \left (t \right ) &= c_{4} {\mathrm e}^{t} \\ \end{align*}

Problem 343

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{3} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-21 x_{3} \left (t \right )-2 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{4} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= -3 c_{4} {\mathrm e}^{2 t}-3 c_{2} {\mathrm e}^{-2 t}+c_{1} {\mathrm e}^{-5 t} \\ x_{3} \left (t \right ) &= c_{3} {\mathrm e}^{5 t} \\ x_{4} \left (t \right ) &= -3 c_{3} {\mathrm e}^{5 t}+c_{2} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 344

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 3, x_{2} \left (0\right ) = 1, x_{3} \left (0\right ) = 1, x_{4} \left (0\right ) = 3] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{15 t}+2 \,{\mathrm e}^{10 t} \\ x_{2} \left (t \right ) &= 2 \,{\mathrm e}^{15 t}-{\mathrm e}^{10 t} \\ x_{3} \left (t \right ) &= 2 \,{\mathrm e}^{15 t}-{\mathrm e}^{10 t} \\ x_{4} \left (t \right ) &= {\mathrm e}^{15 t}+2 \,{\mathrm e}^{10 t} \\ \end{align*}

Problem 345

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= c_{2} {\mathrm e}^{2 t}-\frac {3 c_{3} {\mathrm e}^{5 t}}{2}-\frac {c_{1}}{3} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{2 t}+\frac {c_{3} {\mathrm e}^{5 t}}{2}+\frac {2 c_{1}}{3} \\ \end{align*}

Problem 346

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-20 x_{1} \left (t \right )+11 x_{2} \left (t \right )+13 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=12 x_{1} \left (t \right )-x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-48 x_{1} \left (t \right )+21 x_{2} \left (t \right )+31 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-2 t}+c_{3} {\mathrm e}^{8 t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}-\frac {c_{2} {\mathrm e}^{-2 t}}{3}-c_{3} {\mathrm e}^{8 t} \\ x_{3} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+\frac {5 c_{2} {\mathrm e}^{-2 t}}{3}+3 c_{3} {\mathrm e}^{8 t} \\ \end{align*}

Problem 347

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=147 x_{1} \left (t \right )+23 x_{2} \left (t \right )-202 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-90 x_{1} \left (t \right )-9 x_{2} \left (t \right )+129 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=90 x_{1} \left (t \right )+15 x_{2} \left (t \right )-123 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{6 t} c_{1} +c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{12 t} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{6 t} c_{1}}{7}-\frac {2 c_{2} {\mathrm e}^{-3 t}}{3}-\frac {3 c_{3} {\mathrm e}^{12 t}}{5} \\ x_{3} \left (t \right ) &= \frac {5 \,{\mathrm e}^{6 t} c_{1}}{7}+\frac {2 c_{2} {\mathrm e}^{-3 t}}{3}+\frac {3 c_{3} {\mathrm e}^{12 t}}{5} \\ \end{align*}

Problem 348

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )-7 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-12 x_{1} \left (t \right )+7 x_{2} \left (t \right )+11 x_{3} \left (t \right )+9 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=24 x_{1} \left (t \right )-17 x_{2} \left (t \right )-19 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-18 x_{1} \left (t \right )+13 x_{2} \left (t \right )+17 x_{3} \left (t \right )+9 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{6 t}+c_{4} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{3 t}}{2}-c_{3} {\mathrm e}^{6 t}+c_{4} {\mathrm e}^{-3 t}+2 c_{1} \\ x_{3} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{3 t}}{2}+2 c_{3} {\mathrm e}^{6 t}+c_{4} {\mathrm e}^{-3 t}-c_{1} \\ x_{4} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{3 t}}{2}-c_{3} {\mathrm e}^{6 t}-c_{4} {\mathrm e}^{-3 t}+c_{1} \\ \end{align*}

Problem 349

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=13 x_{1} \left (t \right )-42 x_{2} \left (t \right )+106 x_{3} \left (t \right )+139 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-16 x_{2} \left (t \right )+52 x_{3} \left (t \right )+70 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+6 x_{2} \left (t \right )-20 x_{3} \left (t \right )-31 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-6 x_{2} \left (t \right )+22 x_{3} \left (t \right )+33 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-4 t}+c_{3} {\mathrm e}^{2 t}+c_{4} {\mathrm e}^{8 t} \\ x_{2} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+\frac {2 c_{2} {\mathrm e}^{-4 t}}{3}+2 c_{3} {\mathrm e}^{2 t}-\frac {2 c_{4} {\mathrm e}^{8 t}}{3} \\ x_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{4 t}-\frac {c_{2} {\mathrm e}^{-4 t}}{3}+2 c_{3} {\mathrm e}^{2 t}+c_{4} {\mathrm e}^{8 t} \\ x_{4} \left (t \right ) &= c_{1} {\mathrm e}^{4 t}+\frac {c_{2} {\mathrm e}^{-4 t}}{3}-c_{3} {\mathrm e}^{2 t}-c_{4} {\mathrm e}^{8 t} \\ \end{align*}

Problem 350

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{6 t}+c_{3} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= 2 c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}-c_{3} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{-3 t} \\ x_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}+2 c_{3} {\mathrm e}^{9 t}+\frac {c_{4} {\mathrm e}^{-3 t}}{2} \\ x_{4} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+\frac {c_{2} {\mathrm e}^{6 t}}{2}-c_{3} {\mathrm e}^{9 t}-\frac {c_{4} {\mathrm e}^{-3 t}}{2} \\ \end{align*}

Problem 351

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{48 t}+c_{2} {\mathrm e}^{16 t}+c_{3} {\mathrm e}^{32 t}+c_{4} {\mathrm e}^{64 t} \\ x_{2} \left (t \right ) &= -\frac {c_{1} {\mathrm e}^{48 t}}{3}+2 c_{2} {\mathrm e}^{16 t}+\frac {5 c_{3} {\mathrm e}^{32 t}}{2}+c_{4} {\mathrm e}^{64 t} \\ x_{3} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{48 t}}{3}-c_{2} {\mathrm e}^{16 t}+\frac {c_{3} {\mathrm e}^{32 t}}{2}+2 c_{4} {\mathrm e}^{64 t} \\ x_{4} \left (t \right ) &= \frac {2 c_{1} {\mathrm e}^{48 t}}{3}+2 c_{2} {\mathrm e}^{16 t}-\frac {c_{3} {\mathrm e}^{32 t}}{2}-3 c_{4} {\mathrm e}^{64 t} \\ \end{align*}

Problem 352

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+c_{4} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-3 t} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{6 t} c_{1}}{6}+7 c_{3} {\mathrm e}^{3 t}+c_{2} \\ x_{3} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+\frac {5 c_{4} {\mathrm e}^{9 t}}{2}+3 c_{5} {\mathrm e}^{-3 t} \\ x_{4} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+c_{4} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-3 t}+\frac {{\mathrm e}^{6 t} c_{1}}{6}-\frac {c_{2}}{3} \\ x_{5} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+\frac {{\mathrm e}^{6 t} c_{1}}{6}+\frac {c_{4} {\mathrm e}^{9 t}}{2}+c_{5} {\mathrm e}^{-3 t}+\frac {c_{2}}{3} \\ \end{align*}

Problem 353

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right )\\ x_{6}^{\prime }\left (t \right )&=-14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{5} {\mathrm e}^{-4 t}+c_{6} {\mathrm e}^{9 t} \\ x_{2} \left (t \right ) &= c_{6} {\mathrm e}^{9 t}+c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ x_{3} \left (t \right ) &= {\mathrm e}^{-7 t} c_{3} -{\mathrm e}^{11 t} c_{2} +{\mathrm e}^{5 t} c_{1} \\ x_{4} \left (t \right ) &= {\mathrm e}^{11 t} c_{2} +c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ x_{5} \left (t \right ) &= {\mathrm e}^{11 t} c_{2} +{\mathrm e}^{5 t} c_{1} +c_{5} {\mathrm e}^{-4 t} \\ x_{6} \left (t \right ) &= c_{6} {\mathrm e}^{9 t}+c_{5} {\mathrm e}^{-4 t}+c_{4} {\mathrm e}^{3 t}+{\mathrm e}^{-7 t} c_{3} \\ \end{align*}

Problem 354

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=9 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-6 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{3 t}}{2}-c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{5 t}+c_{1} {\mathrm e}^{3 t} \\ \end{align*}

Problem 355

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+7 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{4 t} \left (3 c_{2} t +3 c_{1} +c_{2} \right )}{3} \\ \end{align*}

Problem 356

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-7 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t -2 c_{3} t +c_{1} -c_{2} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +4 c_{3} t +c_{1} +2 c_{2} -2 c_{3} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ \end{align*}

Problem 357

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )-3 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} +c_{3} {\mathrm e}^{-2 t}+c_{4} {\mathrm e}^{-2 t} t \\ x_{2} \left (t \right ) &= -c_{3} {\mathrm e}^{-2 t}-c_{4} {\mathrm e}^{-2 t} t +c_{4} {\mathrm e}^{-2 t}+c_{2} +c_{1} {\mathrm e}^{-2 t} \\ x_{3} \left (t \right ) &= -{\mathrm e}^{-2 t} \left (2 c_{4} t +2 c_{3} -c_{4} \right ) \\ x_{4} \left (t \right ) &= -{\mathrm e}^{-2 t} \left (-2 c_{4} t +2 c_{1} -2 c_{3} +3 c_{4} \right ) \\ \end{align*}

Problem 358

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-3 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}

Problem 359

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}

Problem 360

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \\ \end{align*}

Problem 361

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{4 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{4 t} \left (c_{2} t +c_{1} +c_{2} \right ) \\ \end{align*}

Problem 362

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{5 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right ) \\ \end{align*}

Problem 363

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{5 t} \left (4 c_{2} t +4 c_{1} +c_{2} \right )}{4} \\ \end{align*}

Problem 364

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-7 x_{1} \left (t \right )+9 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{9 t} \\ x_{3} \left (t \right ) &= c_{2} {\mathrm e}^{2 t} \\ \end{align*}

Problem 365

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=25 x_{1} \left (t \right )+12 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-18 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{7 t}+c_{3} {\mathrm e}^{13 t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{2} {\mathrm e}^{7 t}}{2}-c_{3} {\mathrm e}^{13 t} \\ x_{3} \left (t \right ) &= \frac {c_{2} {\mathrm e}^{7 t}}{2}+\frac {c_{3} {\mathrm e}^{13 t}}{2}+{\mathrm e}^{13 t} c_{1} \\ \end{align*}

Problem 366

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{9 t}+c_{2} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= \frac {c_{1} {\mathrm e}^{9 t}}{3}+\frac {2 c_{2} {\mathrm e}^{5 t}}{7}-\frac {c_{3} {\mathrm e}^{5 t}}{7} \\ \end{align*}

Problem 367

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{7 t} \\ x_{2} \left (t \right ) &= \frac {2 c_{1} {\mathrm e}^{3 t}}{5}+\frac {c_{2} {\mathrm e}^{7 t}}{2}+\frac {6 c_{3} {\mathrm e}^{3 t}}{5} \\ x_{3} \left (t \right ) &= c_{3} {\mathrm e}^{3 t} \\ \end{align*}

Problem 368

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )-4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t +c_{2} \right ) \\ x_{2} \left (t \right ) &= \frac {\left (-c_{3} t^{2}-2 c_{2} t +c_{3} t +4 c_{1} \right ) {\mathrm e}^{-t}}{4} \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{-t} \left (2 c_{3} t +2 c_{2} +c_{3} \right )}{4} \\ \end{align*}

Problem 369

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {\left (c_{3} t^{2}+2 c_{2} t +2 c_{1} \right ) {\mathrm e}^{-t}}{2} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (c_{3} t^{2}+2 c_{2} t +2 c_{1} -2 c_{3} \right )}{2} \\ x_{3} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t +c_{2} \right ) \\ \end{align*}

Problem 370

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )-3 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {\left (c_{3} t^{2}+2 c_{2} t +2 c_{1} \right ) {\mathrm e}^{-t}}{2} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} \left (2 c_{3} t +2 c_{2} +c_{3} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t +c_{2} \right ) \\ \end{align*}

Problem 371

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-5 x_{1} \left (t \right )-x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{-t} \left (5 c_{3} t^{2}+5 c_{2} t +5 c_{1} -2 c_{3} \right ) \\ x_{3} \left (t \right ) &= -{\mathrm e}^{-t} \left (c_{3} t^{2}+c_{2} t -2 c_{3} t +c_{1} -c_{2} \right ) \\ \end{align*}

Problem 372

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-9 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{t} \left (c_{3} t +c_{2} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (3 c_{3} t +3 c_{2} +c_{3} \right )}{9} \\ x_{3} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (-c_{3} t +3 c_{1} -c_{2} \right )}{3} \\ \end{align*}

Problem 373

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+4 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (3 c_{2} t +3 c_{1} +c_{2} +2 c_{3} \right )}{3} \\ \end{align*}

Problem 374

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (6 c_{2} t +6 c_{1} -c_{2} +18 c_{3} \right )}{4} \\ \end{align*}

Problem 375

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ x_{3} \left (t \right ) &= -{\mathrm e}^{t} \left (2 c_{2} t +2 c_{1} -c_{2} +c_{3} \right ) \\ \end{align*}

Problem 376

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right )-x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= c_{4} {\mathrm e}^{t} \\ x_{3} \left (t \right ) &= 3 c_{2} {\mathrm e}^{t}+{\mathrm e}^{-t} c_{1} \\ x_{4} \left (t \right ) &= -2 c_{4} {\mathrm e}^{t}+c_{3} {\mathrm e}^{-t} \\ \end{align*}

Problem 377

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=2 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {\left (c_{4} t^{3}+3 c_{3} t^{2}+6 c_{2} t +6 c_{4} t +6 c_{1} \right ) {\mathrm e}^{2 t}}{6} \\ x_{2} \left (t \right ) &= \frac {\left (c_{4} t^{2}+2 c_{3} t +2 c_{2} \right ) {\mathrm e}^{2 t}}{2} \\ x_{3} \left (t \right ) &= \left (c_{4} t +c_{3} \right ) {\mathrm e}^{2 t} \\ x_{4} \left (t \right ) &= c_{4} {\mathrm e}^{2 t} \\ \end{align*}

Problem 378

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=x_{2} \left (t \right )+x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -{\mathrm e}^{t} \left (2 c_{4} t +2 c_{3} -c_{4} \right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{4} t +c_{3} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{t} \left (c_{4} t +c_{1} +c_{3} \right ) \\ x_{4} \left (t \right ) &= \frac {\left (c_{4} t^{2}+2 c_{3} t +2 c_{2} \right ) {\mathrm e}^{t}}{2} \\ \end{align*}

Problem 379

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{2} \left (t \right )-4 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {\left (-c_{4} t^{2}-2 c_{3} t -7 c_{4} t +4 c_{2} \right ) {\mathrm e}^{t}}{4} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{4} t +c_{3} \right ) \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (2 c_{4} t +2 c_{3} +c_{4} \right )}{4} \\ x_{4} \left (t \right ) &= \frac {\left (c_{4} t^{2}+2 c_{3} t +7 c_{4} t +2 c_{1} \right ) {\mathrm e}^{t}}{2} \\ \end{align*}

Problem 380

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= -c_{2} {\mathrm e}^{3 t}-c_{3} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{3 t} \\ x_{3} \left (t \right ) &= \frac {7 c_{2} {\mathrm e}^{3 t}}{4}+2 c_{3} {\mathrm e}^{-t}+\frac {c_{1} {\mathrm e}^{3 t}}{2} \\ \end{align*}

Problem 381

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= \frac {3 c_{2} {\mathrm e}^{3 t}}{5}+\frac {3 c_{3} {\mathrm e}^{-2 t}}{5}+c_{1} {\mathrm e}^{3 t} \\ x_{3} \left (t \right ) &= -\frac {11 c_{2} {\mathrm e}^{3 t}}{20}-\frac {3 c_{3} {\mathrm e}^{-2 t}}{5}-\frac {c_{1} {\mathrm e}^{3 t}}{2} \\ \end{align*}

Problem 382

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +8 c_{3} t +c_{1} +4 c_{2} -2 c_{3} \right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{2 t} \left (2 c_{3} t +c_{2} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ \end{align*}

Problem 383

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (2 c_{3} t +c_{2} \right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ x_{3} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{3} t^{2}+c_{2} t -4 c_{3} t +c_{1} -2 c_{2} +2 c_{3} \right ) \\ \end{align*}

Problem 384

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t +c_{2} \right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (-3 c_{3} t +5 c_{1} -3 c_{2} \right )}{5} \\ x_{3} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (-8 c_{3} t +5 c_{1} -8 c_{2} -c_{3} \right )}{5} \\ \end{align*}

Problem 385

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{3} t^{2}+c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (833 c_{3} t^{2}+833 c_{2} t +42 c_{3} t +833 c_{1} +21 c_{2} -8 c_{3} \right )}{343} \\ x_{3} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (14 c_{3} t +7 c_{2} +2 c_{3} \right )}{49} \\ \end{align*}

Problem 386

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{4} t +c_{3} \right ) \\ x_{2} \left (t \right ) &= -3 c_{4} {\mathrm e}^{-t} t -3 c_{3} {\mathrm e}^{-t}+c_{4} {\mathrm e}^{-t}+{\mathrm e}^{2 t} t c_{1} +c_{2} {\mathrm e}^{2 t} \\ x_{3} \left (t \right ) &= -c_{4} {\mathrm e}^{-t} t -c_{3} {\mathrm e}^{-t}-{\mathrm e}^{2 t} t c_{1} -2 c_{1} {\mathrm e}^{2 t}-c_{2} {\mathrm e}^{2 t} \\ x_{4} \left (t \right ) &= -2 c_{4} {\mathrm e}^{-t} t -2 c_{3} {\mathrm e}^{-t}-c_{1} {\mathrm e}^{2 t} \\ \end{align*}

Problem 387

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {\left (-c_{2} t +3 c_{1} \right ) {\mathrm e}^{2 t}}{3} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} \left (c_{4} t +c_{3} \right ) \\ x_{3} \left (t \right ) &= \left (-{\mathrm e}^{-3 t} \left (c_{4} t +c_{3} -c_{4} \right )+c_{2} \right ) {\mathrm e}^{2 t} \\ x_{4} \left (t \right ) &= -3 c_{3} {\mathrm e}^{-t}-3 c_{4} {\mathrm e}^{-t} t +2 c_{4} {\mathrm e}^{-t}+\frac {5 c_{2} {\mathrm e}^{2 t}}{3} \\ \end{align*}

Problem 388

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=-27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (-6 c_{4} t^{2}-6 c_{3} t -4 c_{4} t +3 c_{1} -6 c_{2} -2 c_{3} \right )}{3} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (-3 c_{4} t^{2}-3 c_{3} t -16 c_{4} t +3 c_{1} -3 c_{2} -8 c_{3} +6 c_{4} \right )}{9} \\ x_{3} \left (t \right ) &= {\mathrm e}^{t} \left (c_{4} t^{2}+c_{3} t +c_{2} \right ) \\ x_{4} \left (t \right ) &= -\frac {{\mathrm e}^{t} \left (-18 c_{4} t^{2}-18 c_{3} t -6 c_{4} t +9 c_{1} -18 c_{2} -3 c_{3} -2 c_{4} \right )}{9} \\ \end{align*}

Problem 389

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=-48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \left (-\left (c_{3} +c_{5} \right ) {\mathrm e}^{t}+c_{1} \right ) {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= c_{5} {\mathrm e}^{3 t} \\ x_{3} \left (t \right ) &= c_{3} {\mathrm e}^{3 t}+c_{4} {\mathrm e}^{2 t} \\ x_{4} \left (t \right ) &= -\frac {c_{3} {\mathrm e}^{3 t}}{3}-\frac {c_{4} {\mathrm e}^{2 t}}{3}+c_{2} {\mathrm e}^{3 t} \\ x_{5} \left (t \right ) &= \frac {16 c_{3} {\mathrm e}^{3 t}}{3}+8 c_{4} {\mathrm e}^{2 t}+2 c_{2} {\mathrm e}^{3 t}-3 c_{5} {\mathrm e}^{3 t}+3 c_{1} {\mathrm e}^{2 t} \\ \end{align*}

Problem 390

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=3 x_{3} \left (t \right )-4 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=4 x_{3} \left (t \right )+3 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{3 t} \left (4 \cos \left (4 t \right ) c_{4} t +4 \sin \left (4 t \right ) c_{3} t +4 c_{1} \cos \left (4 t \right )+4 c_{2} \sin \left (4 t \right )-\sin \left (4 t \right ) c_{4} \right )}{4} \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (4 \cos \left (4 t \right ) c_{3} t -4 \sin \left (4 t \right ) c_{4} t +4 c_{2} \cos \left (4 t \right )-c_{4} \cos \left (4 t \right )-4 c_{1} \sin \left (4 t \right )\right )}{4} \\ x_{3} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{4} \cos \left (4 t \right )+c_{3} \sin \left (4 t \right )\right ) \\ x_{4} \left (t \right ) &= -{\mathrm e}^{3 t} \left (\cos \left (4 t \right ) c_{3} -\sin \left (4 t \right ) c_{4} \right ) \\ \end{align*}

Problem 391

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-18 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (3 \cos \left (3 t \right ) c_{3} t +3 \cos \left (3 t \right ) c_{4} t +3 \sin \left (3 t \right ) c_{3} t -3 \sin \left (3 t \right ) c_{4} t +3 c_{1} \cos \left (3 t \right )+3 c_{2} \cos \left (3 t \right )+\cos \left (3 t \right ) c_{4} +3 c_{1} \sin \left (3 t \right )-3 c_{2} \sin \left (3 t \right )+\sin \left (3 t \right ) c_{3} \right )}{18} \\ x_{2} \left (t \right ) &= {\mathrm e}^{2 t} \left (\cos \left (3 t \right ) c_{4} t +\sin \left (3 t \right ) c_{3} t +c_{2} \cos \left (3 t \right )+c_{1} \sin \left (3 t \right )\right ) \\ x_{3} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (\cos \left (3 t \right ) c_{3} +\cos \left (3 t \right ) c_{4} +\sin \left (3 t \right ) c_{3} -\sin \left (3 t \right ) c_{4} \right )}{6} \\ x_{4} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (3 \cos \left (3 t \right ) c_{3} t -3 \cos \left (3 t \right ) c_{4} t -3 \sin \left (3 t \right ) c_{3} t -3 \sin \left (3 t \right ) c_{4} t +3 c_{1} \cos \left (3 t \right )-3 c_{2} \cos \left (3 t \right )+10 \cos \left (3 t \right ) c_{3} +9 \cos \left (3 t \right ) c_{4} -3 c_{1} \sin \left (3 t \right )-3 c_{2} \sin \left (3 t \right )+9 \sin \left (3 t \right ) c_{3} -10 \sin \left (3 t \right ) c_{4} \right )}{18} \\ \end{align*}

Problem 392

ODE	\[ \boxed {y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 393

ODE	\[ \boxed {y^{\prime }-4 y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1+4 x +8 x^{2}+\frac {32}{3} x^{3}+\frac {32}{3} x^{4}+\frac {128}{15} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1+4 x +8 x^{2}+\frac {32}{3} x^{3}+\frac {32}{3} x^{4}+\frac {128}{15} x^{5}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+4 x +8 x^{2}+\frac {32}{3} x^{3}+\frac {32}{3} x^{4}+\frac {128}{15} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 394

ODE	\[ \boxed {2 y^{\prime }+3 y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1-\frac {3}{2} x +\frac {9}{8} x^{2}-\frac {9}{16} x^{3}+\frac {27}{128} x^{4}-\frac {81}{1280} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1-\frac {3}{2} x +\frac {9}{8} x^{2}-\frac {9}{16} x^{3}+\frac {27}{128} x^{4}-\frac {81}{1280} x^{5}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1-\frac {3}{2} x +\frac {9}{8} x^{2}-\frac {9}{16} x^{3}+\frac {27}{128} x^{4}-\frac {81}{1280} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 395

ODE	\[ \boxed {2 y x +y^{\prime }=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1-x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1-x^{2}+\frac {1}{2} x^{4}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1-x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 396

ODE	\[ \boxed {y^{\prime }-x^{2} y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1+\frac {x^{3}}{3}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1+\frac {x^{3}}{3}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+\frac {x^{3}}{3}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 397

ODE	\[ \boxed {\left (-2+x \right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1+\frac {1}{2} x +\frac {1}{4} x^{2}+\frac {1}{8} x^{3}+\frac {1}{16} x^{4}+\frac {1}{32} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1+\frac {1}{2} x +\frac {1}{4} x^{2}+\frac {1}{8} x^{3}+\frac {1}{16} x^{4}+\frac {1}{32} x^{5}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+\frac {1}{2} x +\frac {1}{4} x^{2}+\frac {1}{8} x^{3}+\frac {1}{16} x^{4}+\frac {1}{32} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 398

ODE	\[ \boxed {\left (2 x -1\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 399

ODE	\[ \boxed {2 \left (x +1\right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}+\frac {1}{16} x^{3}-\frac {5}{128} x^{4}+\frac {7}{256} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}+\frac {1}{16} x^{3}-\frac {5}{128} x^{4}+\frac {7}{256} x^{5}\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}+\frac {1}{16} x^{3}-\frac {5}{128} x^{4}+\frac {7}{256} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

Problem 400

ODE	\[ \boxed {\left (x -1\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
program solution	\[ y = \left (6 x^{5}+5 x^{4}+4 x^{3}+3 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \] Verified OK. \[ y = \left (6 x^{5}+5 x^{4}+4 x^{3}+3 x^{2}+2 x +1\right ) c_{1} +O\left (x^{6}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (6 x^{5}+5 x^{4}+4 x^{3}+3 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]