2.17.19 Problems 1801 to 1900

Problem 1801

ODE	\[ \boxed {2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \sqrt {t}\, \left (1+\frac {t}{2}+\frac {t^{2}}{40}-\frac {t^{3}}{1680}+\frac {t^{4}}{40320}-\frac {t^{5}}{887040}+O\left (t^{6}\right )\right )+c_{2} \left (1+2 t +\frac {t^{2}}{3}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} \sqrt {t}\, \left (1+\frac {1}{2} t +\frac {1}{40} t^{2}-\frac {1}{1680} t^{3}+\frac {1}{40320} t^{4}-\frac {1}{887040} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (1+2 t +\frac {1}{3} t^{2}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1802

ODE	\[ \boxed {2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1-\frac {t}{3}+\frac {t^{2}}{30}-\frac {t^{3}}{630}+\frac {t^{4}}{22680}-\frac {t^{5}}{1247400}+O\left (t^{6}\right )\right )+c_{2} \sqrt {t}\, \left (1-t +\frac {t^{2}}{6}-\frac {t^{3}}{90}+\frac {t^{4}}{2520}-\frac {t^{5}}{113400}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} \sqrt {t}\, \left (1-t +\frac {1}{6} t^{2}-\frac {1}{90} t^{3}+\frac {1}{2520} t^{4}-\frac {1}{113400} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} t \left (1-\frac {1}{3} t +\frac {1}{30} t^{2}-\frac {1}{630} t^{3}+\frac {1}{22680} t^{4}-\frac {1}{1247400} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1803

ODE	\[ \boxed {4 t y^{\prime \prime }+3 y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t^{\frac {1}{4}} \left (1+\frac {3 t}{5}+\frac {t^{2}}{10}+\frac {t^{3}}{130}+\frac {3 t^{4}}{8840}+\frac {3 t^{5}}{309400}+O\left (t^{6}\right )\right )+c_{2} \left (1+t +\frac {3 t^{2}}{14}+\frac {3 t^{3}}{154}+\frac {3 t^{4}}{3080}+\frac {9 t^{5}}{292600}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t^{\frac {1}{4}} \left (1+\frac {3}{5} t +\frac {1}{10} t^{2}+\frac {1}{130} t^{3}+\frac {3}{8840} t^{4}+\frac {3}{309400} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (1+t +\frac {3}{14} t^{2}+\frac {3}{154} t^{3}+\frac {3}{3080} t^{4}+\frac {9}{292600} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1804

ODE	\[ \boxed {2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1-\frac {t}{3}+\frac {t^{2}}{15}-\frac {t^{3}}{105}+\frac {t^{4}}{945}-\frac {t^{5}}{10395}+O\left (t^{6}\right )\right )+c_{2} \sqrt {t}\, \left (1-\frac {t}{2}+\frac {t^{2}}{8}-\frac {t^{3}}{48}+\frac {t^{4}}{384}-\frac {t^{5}}{3840}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} \sqrt {t}\, \left (1-\frac {1}{2} t +\frac {1}{8} t^{2}-\frac {1}{48} t^{3}+\frac {1}{384} t^{4}-\frac {1}{3840} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} t \left (1-\frac {1}{3} t +\frac {1}{15} t^{2}-\frac {1}{105} t^{3}+\frac {1}{945} t^{4}-\frac {1}{10395} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1805

ODE	\[ \boxed {t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	N/A
Maple solution	\[ \text {No solution found} \]

Problem 1806

ODE	\[ \boxed {t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1+\frac {t}{3}+\frac {t^{2}}{12}+\frac {t^{3}}{60}+\frac {t^{4}}{360}+\frac {t^{5}}{2520}+O\left (t^{6}\right )\right )+\frac {c_{2} \left (1+t +\frac {t^{2}}{2}+\frac {t^{3}}{6}+\frac {t^{4}}{24}+\frac {t^{5}}{120}+O\left (t^{6}\right )\right )}{t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t \left (1+\frac {1}{3} t +\frac {1}{12} t^{2}+\frac {1}{60} t^{3}+\frac {1}{360} t^{4}+\frac {1}{2520} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\frac {c_{2} \left (-2-2 t -t^{2}-\frac {1}{3} t^{3}-\frac {1}{12} t^{4}-\frac {1}{60} t^{5}+\operatorname {O}\left (t^{6}\right )\right )}{t} \]

Problem 1807

ODE	\[ \boxed {t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t^{3} \left (1+\frac {t^{2}}{5}+\frac {t^{4}}{35}+O\left (t^{6}\right )\right )+c_{2} \left (1+\frac {t^{2}}{2}+\frac {t^{4}}{8}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t^{3} \left (1+\frac {1}{5} t^{2}+\frac {1}{35} t^{4}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (12+6 t^{2}+\frac {3}{2} t^{4}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1808

ODE	\[ \boxed {t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-y t=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (1+\frac {t}{3}+\frac {t^{2}}{12}+\frac {t^{3}}{60}+\frac {t^{4}}{360}+\frac {t^{5}}{2520}+O\left (t^{6}\right )\right )+\frac {c_{2} \left (1+t +\frac {t^{2}}{2}+\frac {t^{3}}{6}+\frac {t^{4}}{24}+\frac {t^{5}}{120}+O\left (t^{6}\right )\right )}{t^{2}} \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} \left (1+\frac {1}{3} t +\frac {1}{12} t^{2}+\frac {1}{60} t^{3}+\frac {1}{360} t^{4}+\frac {1}{2520} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\frac {c_{2} \left (-2-2 t -t^{2}-\frac {1}{3} t^{3}-\frac {1}{12} t^{4}-\frac {1}{60} t^{5}+\operatorname {O}\left (t^{6}\right )\right )}{t^{2}} \]

Problem 1809

ODE	\[ \boxed {t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1-\frac {t}{3}+\frac {t^{2}}{12}-\frac {t^{3}}{60}+\frac {t^{4}}{360}-\frac {t^{5}}{2520}+O\left (t^{6}\right )\right )+\frac {c_{2} \left (1-t +\frac {t^{2}}{2}-\frac {t^{3}}{6}+\frac {t^{4}}{24}-\frac {t^{5}}{120}+O\left (t^{6}\right )\right )}{t} \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t \left (1-\frac {1}{3} t +\frac {1}{12} t^{2}-\frac {1}{60} t^{3}+\frac {1}{360} t^{4}-\frac {1}{2520} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\frac {c_{2} \left (-2+2 t -t^{2}+\frac {1}{3} t^{3}-\frac {1}{12} t^{4}+\frac {1}{60} t^{5}+\operatorname {O}\left (t^{6}\right )\right )}{t} \]

Problem 1810

ODE	\[ \boxed {t y^{\prime \prime }-y^{\prime } \left (t +4\right )+2 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t^{5} \left (1+\frac {t}{2}+\frac {t^{2}}{7}+\frac {5 t^{3}}{168}+\frac {5 t^{4}}{1008}+\frac {t^{5}}{1440}+O\left (t^{6}\right )\right )+c_{2} \left (1+\frac {t}{2}+\frac {t^{2}}{12}+\frac {t^{5}}{720}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t^{5} \left (1+\frac {1}{2} t +\frac {1}{7} t^{2}+\frac {5}{168} t^{3}+\frac {5}{1008} t^{4}+\frac {1}{1440} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (2880+1440 t +240 t^{2}+4 t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1811

ODE	\[ \boxed {t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t^{3} \left (1-t +\frac {t^{2}}{2}-\frac {t^{3}}{6}+\frac {t^{4}}{24}-\frac {t^{5}}{120}+O\left (t^{6}\right )\right )+c_{2} \left (-t^{3} \left (1-t +\frac {t^{2}}{2}-\frac {t^{3}}{6}+\frac {t^{4}}{24}-\frac {t^{5}}{120}+O\left (t^{6}\right )\right ) \ln \left (t \right )+t \left (1+t -t^{3}+\frac {3 t^{4}}{4}-\frac {11 t^{5}}{36}+O\left (t^{6}\right )\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (c_{1} t^{2} \left (1-t +\frac {1}{2} t^{2}-\frac {1}{6} t^{3}+\frac {1}{24} t^{4}-\frac {1}{120} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (\ln \left (t \right ) \left (2 t^{2}-2 t^{3}+t^{4}-\frac {1}{3} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (-2-2 t +3 t^{2}-t^{3}+\frac {1}{9} t^{5}+\operatorname {O}\left (t^{6}\right )\right )\right )\right ) t \]

Problem 1812

ODE	\[ \boxed {t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1+\frac {t}{3}+\frac {t^{2}}{24}+\frac {t^{3}}{360}+\frac {t^{4}}{8640}+\frac {t^{5}}{302400}+O\left (t^{6}\right )\right )+c_{2} \left (-\frac {t \left (1+\frac {t}{3}+\frac {t^{2}}{24}+\frac {t^{3}}{360}+\frac {t^{4}}{8640}+\frac {t^{5}}{302400}+O\left (t^{6}\right )\right ) \ln \left (t \right )}{2}+\frac {1-t +\frac {2 t^{3}}{9}+\frac {25 t^{4}}{576}+\frac {157 t^{5}}{43200}+O\left (t^{6}\right )}{t}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \frac {c_{1} t^{2} \left (1+\frac {1}{3} t +\frac {1}{24} t^{2}+\frac {1}{360} t^{3}+\frac {1}{8640} t^{4}+\frac {1}{302400} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (\ln \left (t \right ) \left (t^{2}+\frac {1}{3} t^{3}+\frac {1}{24} t^{4}+\frac {1}{360} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (-2+2 t -\frac {4}{9} t^{3}-\frac {25}{288} t^{4}-\frac {157}{21600} t^{5}+\operatorname {O}\left (t^{6}\right )\right )\right )}{t} \]

Problem 1813

ODE	\[ \boxed {t y^{\prime \prime }+t y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1-\frac {3 t}{2}+t^{2}-\frac {5 t^{3}}{12}+\frac {t^{4}}{8}-\frac {7 t^{5}}{240}+O\left (t^{6}\right )\right )+c_{2} \left (-2 t \left (1-\frac {3 t}{2}+t^{2}-\frac {5 t^{3}}{12}+\frac {t^{4}}{8}-\frac {7 t^{5}}{240}+O\left (t^{6}\right )\right ) \ln \left (t \right )+1-\frac {7 t^{2}}{2}+\frac {7 t^{3}}{2}-\frac {16 t^{4}}{9}+\frac {29 t^{5}}{48}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t \left (1-\frac {3}{2} t +t^{2}-\frac {5}{12} t^{3}+\frac {1}{8} t^{4}-\frac {7}{240} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (\ln \left (t \right ) \left (\left (-2\right ) t +3 t^{2}-2 t^{3}+\frac {5}{6} t^{4}-\frac {1}{4} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (1-t -2 t^{2}+\frac {5}{2} t^{3}-\frac {49}{36} t^{4}+\frac {23}{48} t^{5}+\operatorname {O}\left (t^{6}\right )\right )\right ) \]

Problem 1814

ODE	\[ \boxed {t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 y t=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (-t^{2}+1+\frac {t^{4}}{8}+O\left (t^{6}\right )\right )+c_{2} \left (\left (-t^{2}+1+\frac {t^{4}}{8}+O\left (t^{6}\right )\right ) \ln \left (t \right )+\frac {5 t^{2}}{4}-\frac {9 t^{4}}{32}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (c_{2} \ln \left (t \right )+c_{1} \right ) \left (1-t^{2}+\frac {1}{8} t^{4}+\operatorname {O}\left (t^{6}\right )\right )+\left (\frac {5}{4} t^{2}-\frac {9}{32} t^{4}+\operatorname {O}\left (t^{6}\right )\right ) c_{2} \]

Problem 1815

ODE	\[ \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+y t^{2}=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (1-\frac {t^{2}}{4}+\frac {t^{4}}{64}+O\left (t^{6}\right )\right )+c_{2} \left (\left (1-\frac {t^{2}}{4}+\frac {t^{4}}{64}+O\left (t^{6}\right )\right ) \ln \left (t \right )+\frac {t^{2}}{4}-\frac {3 t^{4}}{128}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (c_{2} \ln \left (t \right )+c_{1} \right ) \left (1-\frac {1}{4} t^{2}+\frac {1}{64} t^{4}+\operatorname {O}\left (t^{6}\right )\right )+\left (\frac {1}{4} t^{2}-\frac {3}{128} t^{4}+\operatorname {O}\left (t^{6}\right )\right ) c_{2} \]

Problem 1816

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

Problem 1817

ODE	\[ \boxed {t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (-\lambda t +1+\frac {\left (\lambda -1\right ) \lambda \,t^{2}}{4}-\frac {\left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{3}}{36}+\frac {\left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{4}}{576}-\frac {\left (\lambda -4\right ) \left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{5}}{14400}+O\left (t^{6}\right )\right )+c_{2} \left (\left (-\lambda t +1+\frac {\left (\lambda -1\right ) \lambda \,t^{2}}{4}-\frac {\left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{3}}{36}+\frac {\left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{4}}{576}-\frac {\left (\lambda -4\right ) \left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right ) \lambda \,t^{5}}{14400}+O\left (t^{6}\right )\right ) \ln \left (t \right )+\left (1+2 \lambda \right ) t +\left (-\frac {\lambda }{2}+\frac {1}{4}-\frac {3 \left (\lambda -1\right ) \lambda }{4}\right ) t^{2}+\left (-\frac {\left (1-\lambda \right ) \lambda }{36}-\frac {\left (-\lambda +2\right ) \lambda }{36}+\frac {\left (-\lambda +2\right ) \left (1-\lambda \right )}{36}+\frac {11 \left (-\lambda +2\right ) \left (1-\lambda \right ) \lambda }{108}\right ) t^{3}+\left (-\frac {\left (\lambda -2\right ) \left (\lambda -1\right ) \lambda }{576}-\frac {\left (\lambda -3\right ) \left (\lambda -1\right ) \lambda }{576}-\frac {\left (\lambda -3\right ) \left (\lambda -2\right ) \lambda }{576}-\frac {\left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right )}{576}-\frac {25 \left (\lambda -3\right ) \left (\lambda -2\right ) \left (\lambda -1\right ) \lambda }{3456}\right ) t^{4}+\left (-\frac {\left (3-\lambda \right ) \left (-\lambda +2\right ) \left (1-\lambda \right ) \lambda }{14400}-\frac {\left (4-\lambda \right ) \left (-\lambda +2\right ) \left (1-\lambda \right ) \lambda }{14400}-\frac {\left (4-\lambda \right ) \left (3-\lambda \right ) \left (1-\lambda \right ) \lambda }{14400}-\frac {\left (4-\lambda \right ) \left (3-\lambda \right ) \left (-\lambda +2\right ) \lambda }{14400}+\frac {\left (4-\lambda \right ) \left (3-\lambda \right ) \left (-\lambda +2\right ) \left (1-\lambda \right )}{14400}+\frac {137 \left (4-\lambda \right ) \left (3-\lambda \right ) \left (-\lambda +2\right ) \left (1-\lambda \right ) \lambda }{432000}\right ) t^{5}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (\left (2 \lambda +1\right ) t +\left (\frac {1}{4} \lambda +\frac {1}{4}-\frac {3}{4} \lambda ^{2}\right ) t^{2}+\left (-\frac {2}{9} \lambda ^{2}+\frac {1}{27} \lambda +\frac {1}{18}+\frac {11}{108} \lambda ^{3}\right ) t^{3}+\left (\frac {7}{192} \lambda ^{3}-\frac {167}{3456} \lambda ^{2}+\frac {1}{192} \lambda +\frac {1}{96}-\frac {25}{3456} \lambda ^{4}\right ) t^{4}+\left (\frac {719}{86400} \lambda ^{3}-\frac {61}{21600} \lambda ^{4}+\frac {137}{432000} \lambda ^{5}+\frac {1}{1500} \lambda -\frac {37}{4320} \lambda ^{2}+\frac {1}{600}\right ) t^{5}+\operatorname {O}\left (t^{6}\right )\right ) c_{2} +\left (1-\lambda t +\frac {1}{4} \left (-1+\lambda \right ) \lambda t^{2}-\frac {1}{36} \left (\lambda -2\right ) \left (-1+\lambda \right ) \lambda t^{3}+\frac {1}{576} \left (\lambda -3\right ) \left (\lambda -2\right ) \left (-1+\lambda \right ) \lambda t^{4}-\frac {1}{14400} \left (\lambda -4\right ) \left (\lambda -3\right ) \left (\lambda -2\right ) \left (-1+\lambda \right ) \lambda t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \left (c_{2} \ln \left (t \right )+c_{1} \right ) \]

Problem 1818

ODE	\[ \boxed {2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \sqrt {t}\, \left (1+\frac {5 t}{6}+\frac {17 t^{2}}{60}+\frac {89 t^{3}}{1260}+\frac {941 t^{4}}{45360}+\frac {14989 t^{5}}{2494800}+O\left (t^{6}\right )\right )+c_{2} \left (1+2 t +t^{2}+\frac {4 t^{3}}{15}+\frac {t^{4}}{14}+\frac {101 t^{5}}{4725}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} \sqrt {t}\, \left (1+\frac {5}{6} t +\frac {17}{60} t^{2}+\frac {89}{1260} t^{3}+\frac {941}{45360} t^{4}+\frac {14989}{2494800} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (1+2 t +t^{2}+\frac {4}{15} t^{3}+\frac {1}{14} t^{4}+\frac {101}{4725} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1819

ODE	\[ \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t^{i} \left (1+\left (-\frac {1}{5}+\frac {2 i}{5}\right ) t +\left (-\frac {1}{40}-\frac {3 i}{40}\right ) t^{2}+\left (\frac {3}{520}+\frac {7 i}{1560}\right ) t^{3}+\left (-\frac {1}{2496}-\frac {i}{12480}\right ) t^{4}+\left (\frac {9}{603200}-\frac {i}{361920}\right ) t^{5}+O\left (t^{6}\right )\right )+c_{2} t^{-i} \left (1+\left (-\frac {1}{5}-\frac {2 i}{5}\right ) t +\left (-\frac {1}{40}+\frac {3 i}{40}\right ) t^{2}+\left (\frac {3}{520}-\frac {7 i}{1560}\right ) t^{3}+\left (-\frac {1}{2496}+\frac {i}{12480}\right ) t^{4}+\left (\frac {9}{603200}+\frac {i}{361920}\right ) t^{5}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = c_{1} t^{-i} \left (1+\left (-\frac {1}{5}-\frac {2 i}{5}\right ) t +\left (-\frac {1}{40}+\frac {3 i}{40}\right ) t^{2}+\left (\frac {3}{520}-\frac {7 i}{1560}\right ) t^{3}+\left (-\frac {1}{2496}+\frac {i}{12480}\right ) t^{4}+\left (\frac {9}{603200}+\frac {i}{361920}\right ) t^{5}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} t^{i} \left (1+\left (-\frac {1}{5}+\frac {2 i}{5}\right ) t +\left (-\frac {1}{40}-\frac {3 i}{40}\right ) t^{2}+\left (\frac {3}{520}+\frac {7 i}{1560}\right ) t^{3}+\left (-\frac {1}{2496}-\frac {i}{12480}\right ) t^{4}+\left (\frac {9}{603200}-\frac {i}{361920}\right ) t^{5}+\operatorname {O}\left (t^{6}\right )\right ) \]

Problem 1820

ODE	\[ \boxed {t y^{\prime \prime }+y^{\prime }-4 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (4 t^{2}+4 t +1+\frac {16 t^{3}}{9}+\frac {4 t^{4}}{9}+\frac {16 t^{5}}{225}+O\left (t^{6}\right )\right )+c_{2} \left (\left (4 t^{2}+4 t +1+\frac {16 t^{3}}{9}+\frac {4 t^{4}}{9}+\frac {16 t^{5}}{225}+O\left (t^{6}\right )\right ) \ln \left (t \right )-12 t^{2}-8 t -\frac {176 t^{3}}{27}-\frac {50 t^{4}}{27}-\frac {1096 t^{5}}{3375}+O\left (t^{6}\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (c_{2} \ln \left (t \right )+c_{1} \right ) \left (1+4 t +4 t^{2}+\frac {16}{9} t^{3}+\frac {4}{9} t^{4}+\frac {16}{225} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (\left (-8\right ) t -12 t^{2}-\frac {176}{27} t^{3}-\frac {50}{27} t^{4}-\frac {1096}{3375} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) c_{2} \]

Problem 1821

ODE	\[ \boxed {t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1+t +\frac {t^{2}}{2}+\frac {t^{3}}{6}+\frac {t^{4}}{24}+\frac {t^{5}}{120}+O\left (t^{6}\right )\right )+c_{2} \left (t \left (1+t +\frac {t^{2}}{2}+\frac {t^{3}}{6}+\frac {t^{4}}{24}+\frac {t^{5}}{120}+O\left (t^{6}\right )\right ) \ln \left (t \right )+t \left (-t -\frac {3 t^{2}}{4}-\frac {11 t^{3}}{36}-\frac {25 t^{4}}{288}-\frac {137 t^{5}}{7200}+O\left (t^{6}\right )\right )\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \left (\left (c_{2} \ln \left (t \right )+c_{1} \right ) \left (1+t +\frac {1}{2} t^{2}+\frac {1}{6} t^{3}+\frac {1}{24} t^{4}+\frac {1}{120} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (-t -\frac {3}{4} t^{2}-\frac {11}{36} t^{3}-\frac {25}{288} t^{4}-\frac {137}{7200} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) c_{2} \right ) t \]

Problem 1822

ODE	\[ \boxed {t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} t \left (1-\frac {t^{2}}{8}+\frac {t^{4}}{192}+O\left (t^{6}\right )\right )+c_{2} \left (-\frac {t \left (1-\frac {t^{2}}{8}+\frac {t^{4}}{192}+O\left (t^{6}\right )\right ) \ln \left (t \right )}{2}+\frac {1-\frac {3 t^{4}}{64}+O\left (t^{6}\right )}{t}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \frac {c_{1} t^{2} \left (1-\frac {1}{8} t^{2}+\frac {1}{192} t^{4}+\operatorname {O}\left (t^{6}\right )\right )+c_{2} \left (\ln \left (t \right ) \left (t^{2}-\frac {1}{8} t^{4}+\operatorname {O}\left (t^{6}\right )\right )+\left (-2+\frac {3}{32} t^{4}+\operatorname {O}\left (t^{6}\right )\right )\right )}{t} \]

Problem 1823

ODE	\[ \boxed {t y^{\prime \prime }+3 y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(t = 0\).
program solution	\[ y = c_{1} \left (1+t +\frac {3 t^{2}}{8}+\frac {3 t^{3}}{40}+\frac {3 t^{4}}{320}+\frac {9 t^{5}}{11200}+O\left (t^{6}\right )\right )+c_{2} \left (\left (-\frac {9}{2}-\frac {9 t}{2}-\frac {27 t^{2}}{16}-\frac {27 t^{3}}{80}-\frac {27 t^{4}}{640}-\frac {81 t^{5}}{22400}-\frac {9 O\left (t^{6}\right )}{2}\right ) \ln \left (t \right )+\frac {1-3 t +6 t^{3}+\frac {225 t^{4}}{64}+\frac {1413 t^{5}}{1600}+O\left (t^{6}\right )}{t^{2}}\right ) \] Verified OK.
Maple solution	\[ y \left (t \right ) = \frac {c_{1} \left (1+t +\frac {3}{8} t^{2}+\frac {3}{40} t^{3}+\frac {3}{320} t^{4}+\frac {9}{11200} t^{5}+\operatorname {O}\left (t^{6}\right )\right ) t^{2}+c_{2} \left (\ln \left (t \right ) \left (9 t^{2}+9 t^{3}+\frac {27}{8} t^{4}+\frac {27}{40} t^{5}+\operatorname {O}\left (t^{6}\right )\right )+\left (-2+6 t -12 t^{3}-\frac {225}{32} t^{4}-\frac {1413}{800} t^{5}+\operatorname {O}\left (t^{6}\right )\right )\right )}{t^{2}} \]

Problem 1824

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

Problem 1825

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 )&=-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}^{-t} c_{1} +c_{2} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} c_{1} +4 c_{2} {\mathrm e}^{2 t} \\ \end{align*}

Problem 1826

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

Problem 1827

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-2 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 ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{5 t} \\ x_{2} \left (t \right ) &= -2 c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{2 t}-2 c_{3} {\mathrm e}^{5 t} \\ x_{3} \left (t \right ) &= -c_{1} {\mathrm e}^{3 t}-c_{2} {\mathrm e}^{2 t}-\frac {2 c_{3} {\mathrm e}^{5 t}}{3} \\ \end{align*}

Problem 1828

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-7 x_{1} \left (t \right )+6 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=6 x_{1} \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}^{-10 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}^{-10 t}}{2}+2 c_{2} {\mathrm e}^{5 t} \\ \end{align*}

Problem 1829

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+6 x_{4} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+9 x_{3} \left (t \right )+18 x_{4} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+10 x_{2} \left (t \right )+15 x_{3} \left (t \right )+30 x_{4} \left (t \right )\\ x_{4}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+14 x_{2} \left (t \right )+21 x_{3} \left (t \right )+42 x_{4} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= c_{3} +c_{4} {\mathrm e}^{64 t} \\ x_{2} \left (t \right ) &= 3 c_{3} +3 c_{4} {\mathrm e}^{64 t}+c_{2} \\ x_{3} \left (t \right ) &= 5 c_{3} +5 c_{4} {\mathrm e}^{64 t}+c_{1} \\ x_{4} \left (t \right ) &= 7 c_{4} {\mathrm e}^{64 t}-\frac {11 c_{3}}{3}-\frac {c_{2}}{3}-\frac {c_{1}}{2} \\ \end{align*}

Problem 1830

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

Problem 1831

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

Problem 1832

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

Problem 1833

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=x_{1} \left (t \right )+10 x_{2} \left (t \right )+2 x_{3} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = -1, x_{2} \left (0\right ) = -4, x_{3} \left (0\right ) = 13] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{t}-2 \,{\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= -4 \,{\mathrm e}^{-t} \\ x_{3} \left (t \right ) &= -{\mathrm e}^{t}+14 \,{\mathrm e}^{-t} \\ \end{align*}

Problem 1834

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

Problem 1835

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 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 )-3 x_{3} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 4, x_{3} \left (0\right ) = -7] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= 9 \,{\mathrm e}^{t}-\frac {28 \,{\mathrm e}^{-t}}{3}+\frac {4 \,{\mathrm e}^{2 t}}{3} \\ x_{2} \left (t \right ) &= \frac {8 \,{\mathrm e}^{-t}}{3}+\frac {4 \,{\mathrm e}^{2 t}}{3} \\ x_{3} \left (t \right ) &= 9 \,{\mathrm e}^{t}-\frac {52 \,{\mathrm e}^{-t}}{3}+\frac {4 \,{\mathrm e}^{2 t}}{3} \\ \end{align*}

Problem 1836

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 )&=-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 (t \right )+c_{2} \cos \left (t \right )\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-2 t} \left (c_{1} \sin \left (t \right )-c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+c_{2} \cos \left (t \right )\right )}{2} \\ \end{align*}

Problem 1837

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

Problem 1838

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

Problem 1839

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

Problem 1840

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

Problem 1841

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

Problem 1842

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

Problem 1843

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

Problem 1844

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

Problem 1845

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

Problem 1846

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

Problem 1847

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

Problem 1848

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

Problem 1849

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

Problem 1850

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

Problem 1851

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=10 x_{1} \left (t \right )+9 x_{2} \left (t \right )+x_{3} \left (t \right )\\ x_{3}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 2, x_{2} \left (0\right ) = 1, x_{3} \left (0\right ) = -1] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (-4 t^{2}-16 t +2\right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{2 t} \left (-24 t^{2}-104 t -4\right )}{4} \\ x_{3} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (-8 t^{2}-40 t -4\right )}{4} \\ \end{align*}

Problem 1852

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

Problem 1853

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

Problem 1854

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

Problem 1855

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+{\mathrm e}^{c t}\\ 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 )&=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 ) &= c_{3} {\mathrm e}^{t}+\frac {{\mathrm e}^{c t}}{c -1} \\ x_{2} \left (t \right ) &= \frac {2 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{2} c^{3}+2 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{1} c^{3}-3 c^{3} {\mathrm e}^{t} c_{3} \cos \left (2 t \right )-6 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{2} c^{2}-6 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{1} c^{2}+9 c^{2} {\mathrm e}^{t} c_{3} \cos \left (2 t \right )-3 c^{3} {\mathrm e}^{t} c_{3} +14 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{2} c +14 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{1} c -21 \,{\mathrm e}^{t} c_{3} c \cos \left (2 t \right )+9 c^{2} {\mathrm e}^{t} c_{3} -10 c_{2} {\mathrm e}^{t} \sin \left (2 t \right )-10 c_{1} {\mathrm e}^{t} \cos \left (2 t \right )+15 \,{\mathrm e}^{t} c_{3} \cos \left (2 t \right )-21 \,{\mathrm e}^{t} c_{3} c +4 c \,{\mathrm e}^{t +t \left (c -1\right )}+15 c_{3} {\mathrm e}^{t}-16 \,{\mathrm e}^{t +t \left (c -1\right )}}{2 \left (c -1\right ) \left (c^{2}-2 c +5\right )} \\ x_{3} \left (t \right ) &= \frac {2 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{1} c^{3}-3 c^{3} {\mathrm e}^{t} c_{3} \sin \left (2 t \right )-2 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{2} c^{3}-6 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{1} c^{2}+9 c^{2} {\mathrm e}^{t} c_{3} \sin \left (2 t \right )+6 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{2} c^{2}+2 c^{3} {\mathrm e}^{t} c_{3} +14 \,{\mathrm e}^{t} \sin \left (2 t \right ) c_{1} c -21 \,{\mathrm e}^{t} c_{3} c \sin \left (2 t \right )-14 \,{\mathrm e}^{t} \cos \left (2 t \right ) c_{2} c -6 c^{2} {\mathrm e}^{t} c_{3} -10 c_{1} {\mathrm e}^{t} \sin \left (2 t \right )+15 \sin \left (2 t \right ) {\mathrm e}^{t} c_{3} +10 c_{2} {\mathrm e}^{t} \cos \left (2 t \right )+14 \,{\mathrm e}^{t} c_{3} c -10 c_{3} {\mathrm e}^{t}+6 \,{\mathrm e}^{c t} c +2 \,{\mathrm e}^{c t}}{2 \left (c -1\right ) \left (c^{2}-2 c +5\right )} \\ \end{align*}

Problem 1856

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-2 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 0] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (12 \sin \left (t \right ) t +4 \cos \left (t \right ) t +4 \sin \left (t \right )\right )}{2} \\ x_{2} \left (t \right ) &= -4 \,{\mathrm e}^{t} \sin \left (t \right ) t \\ \end{align*}

Problem 1857

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

Problem 1858

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 0] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -4 \sin \left (t \right )+5 \cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right )-\cos \left (t \right ) t +\frac {\sin \left (t \right ) t}{2} \\ x_{2} \left (t \right ) &= \frac {10 \sin \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \sec \left (t \right )+20 \cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \sec \left (t \right )-15 \sin \left (t \right ) \sec \left (t \right )-10 \sec \left (t \right ) \cos \left (t \right ) \tan \left (t \right )+10 \cos \left (t \right ) \sec \left (t \right )-5 \cos \left (t \right ) t \sec \left (t \right )+10 \sin \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \tan \left (t \right )+20 \cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \tan \left (t \right )-15 \sin \left (t \right ) \tan \left (t \right )-10 \cos \left (t \right ) \tan \left (t \right )^{2}+10 \cos \left (t \right ) \tan \left (t \right )-5 \cos \left (t \right ) t \tan \left (t \right )-10 \cos \left (t \right )}{10 \sec \left (t \right )+10 \tan \left (t \right )} \\ \end{align*}

Problem 1859

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{2} \left (t \right )+f_{1} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+f_{2} \left (t \right ) \end {align*} With initial conditions \[ [x_{1} \left (0\right ) = 0, x_{2} \left (0\right ) = 0] \]
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= f_{1} \left (0\right ) \sin \left (t \right )+\left (\int _{0}^{t}\cos \left (\textit {\_z1} \right ) \left (\frac {d}{d \textit {\_z1}}f_{1} \left (\textit {\_z1} \right )+f_{2} \left (\textit {\_z1} \right )\right )d \textit {\_z1} \right ) \sin \left (t \right )-\left (\int _{0}^{t}\sin \left (\textit {\_z1} \right ) \left (\frac {d}{d \textit {\_z1}}f_{1} \left (\textit {\_z1} \right )+f_{2} \left (\textit {\_z1} \right )\right )d \textit {\_z1} \right ) \cos \left (t \right ) \\ x_{2} \left (t \right ) &= f_{1} \left (0\right ) \cos \left (t \right )+\left (\int _{0}^{t}\cos \left (\textit {\_z1} \right ) \left (\frac {d}{d \textit {\_z1}}f_{1} \left (\textit {\_z1} \right )+f_{2} \left (\textit {\_z1} \right )\right )d \textit {\_z1} \right ) \cos \left (t \right )+\left (\int _{0}^{t}\sin \left (\textit {\_z1} \right ) \left (\frac {d}{d \textit {\_z1}}f_{1} \left (\textit {\_z1} \right )+f_{2} \left (\textit {\_z1} \right )\right )d \textit {\_z1} \right ) \sin \left (t \right )-f_{1} \left (t \right ) \\ \end{align*}

Problem 1860

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

Problem 1861

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

Problem 1862

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

Problem 1863

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

Problem 1864

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+\sin \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-x_{1} \left (t \right )+2 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 )-x_{3} \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -\frac {\sin \left (t \right )}{10}-\frac {\cos \left (t \right )}{5}+c_{1} {\mathrm e}^{3 t}-\frac {c_{2} {\mathrm e}^{t}}{2}+c_{3} {\mathrm e}^{-2 t} \\ x_{2} \left (t \right ) &= c_{3} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{t}+\frac {\cos \left (t \right )}{10}+\frac {3 \sin \left (t \right )}{10} \\ x_{3} \left (t \right ) &= -\frac {4 \sin \left (t \right )}{5}-\frac {\cos \left (t \right )}{10}+c_{1} {\mathrm e}^{3 t}-\frac {3 c_{2} {\mathrm e}^{t}}{2}-3 c_{3} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 1865

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

Problem 1866

ODE	\begin {align*} x_{1}^{\prime }\left (t \right )&=-x_{1} \left (t \right )-x_{2} \left (t \right )+1\\ x_{2}^{\prime }\left (t \right )&=-4 x_{2} \left (t \right )-x_{3} \left (t \right )+t\\ x_{3}^{\prime }\left (t \right )&=5 x_{2} \left (t \right )+{\mathrm e}^{t} \end {align*}
program solution
Maple solution	\begin{align*} x_{1} \left (t \right ) &= -\frac {c_{2} {\mathrm e}^{-2 t} \sin \left (t \right )}{2}+\frac {{\mathrm e}^{-2 t} \sin \left (t \right ) c_{3}}{2}+\frac {c_{2} {\mathrm e}^{-2 t} \cos \left (t \right )}{2}+\frac {{\mathrm e}^{-2 t} \cos \left (t \right ) c_{3}}{2}+\frac {{\mathrm e}^{t}}{20}+\frac {4}{5}+{\mathrm e}^{-t} c_{1} \\ x_{2} \left (t \right ) &= {\mathrm e}^{-2 t} \sin \left (t \right ) c_{3} +c_{2} {\mathrm e}^{-2 t} \cos \left (t \right )+\frac {1}{5}-\frac {{\mathrm e}^{t}}{10} \\ x_{3} \left (t \right ) &= -2 \,{\mathrm e}^{-2 t} \sin \left (t \right ) c_{3} -{\mathrm e}^{-2 t} \cos \left (t \right ) c_{3} -2 c_{2} {\mathrm e}^{-2 t} \cos \left (t \right )+c_{2} {\mathrm e}^{-2 t} \sin \left (t \right )+\frac {{\mathrm e}^{t}}{2}-\frac {4}{5}+t \\ \end{align*}

Problem 1867

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

Problem 1868

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

Problem 1869

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

Problem 1870

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

Problem 1871

ODE	\[ \boxed {x y^{2}+\left (y-x^{2} y\right ) y^{\prime }=-x} \]
program solution	\[ -\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2}+\frac {\ln \left (1+y^{2}\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x^{2}-c_{1} -1} \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}-c_{1} -1} \\ \end{align*}

Problem 1872

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

Problem 1873

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

Problem 1874

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

Problem 1875

ODE	\[ \boxed {x y^{2}+\left (x^{2} y-y\right ) y^{\prime }=-x} \]
program solution	\[ -\frac {\ln \left (x -1\right )}{2}-\frac {\ln \left (x +1\right )}{2}-\frac {\ln \left (1+y^{2}\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_{1} \right )}}{x^{2}-1} \\ y \left (x \right ) &= -\frac {\sqrt {\left (x^{2}-1\right ) \left (-x^{2}+c_{1} \right )}}{x^{2}-1} \\ \end{align*}

Problem 1876

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

Problem 1877

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

Problem 1878

ODE	\[ \boxed {y^{\prime } \tan \left (x \right )-y=1} \]
program solution	\[ y = \sin \left (x \right ) {\mathrm e}^{c_{1}}-1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = c_{1} \sin \left (x \right )-1 \]

Problem 1879

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

Problem 1880

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

Problem 1881

ODE	\[ \boxed {x^{\prime }=1-\sin \left (2 t \right )} \]
program solution	\[ x = t +\frac {\cos \left (2 t \right )}{2}+c_{1} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \frac {\cos \left (2 t \right )}{2}+t +c_{1} \]

Problem 1882

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

Problem 1883

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

Problem 1884

ODE	\[ \boxed {\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }=0} \]
program solution	\[ y = \operatorname {arcsec}\left (\tan \left (x \right )+c_{1} \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arccos \left (\frac {1}{\tan \left (x \right )+c_{1}}\right ) \]

Problem 1885

ODE	\[ \boxed {y+y^{\prime } x -x y \left (y^{\prime }-1\right )=0} \]
program solution	\[ y = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x -c_{1}}}{x}\right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-x}}{c_{1} x}\right ) \]

Problem 1886

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

Problem 1887

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

Problem 1888

ODE	\[ \boxed {\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }=-\tan \left (x \right ) \sin \left (x \right )^{2}} \]
program solution	\[ -\frac {\tan \left (x \right )^{2}}{2}-\ln \left (\cos \left (x \right )\right )-\ln \left (\sin \left (y\right )\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \arcsin \left (\frac {\sqrt {2}\, \sqrt {\frac {1}{1+\cos \left (2 x \right )}}\, {\mathrm e}^{\frac {-1+\cos \left (2 x \right )}{2+2 \cos \left (2 x \right )}}}{c_{1}}\right ) \]

Problem 1889

ODE	\[ \boxed {y^{2}+y y^{\prime }+y^{\prime } x^{2} y=1} \]
program solution	\[ -\arctan \left (x \right )-\frac {\ln \left (y-1\right )}{2}-\frac {\ln \left (1+y\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-2 \arctan \left (x \right )} c_{1} +1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-2 \arctan \left (x \right )} c_{1} +1} \\ \end{align*}

Problem 1890

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

Problem 1891

ODE	\[ \boxed {y^{\prime } x +2 y=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 1] \end {align*}
program solution	\[ y = \frac {4}{x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {4}{x^{2}} \]

Problem 1892

ODE	\[ \boxed {\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ \ln \left (\cos \left (x \right )\right )+\ln \left (\cos \left (y\right )\right ) = 0 \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\pi }{2}-\arcsin \left (\sec \left (x \right )\right ) \\ y \left (x \right ) &= -\frac {\pi }{2}+\arcsin \left (\sec \left (x \right )\right ) \\ \end{align*}

Problem 1893

ODE	\[ \boxed {y^{\prime } x^{2}+y^{2}=0} \] With initial conditions \begin {align*} [y \left (3\right ) = 1] \end {align*}
program solution	\[ y = \frac {3 x}{4 x -3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {3 x}{4 x -3} \]

Problem 1894

ODE	\[ \boxed {y^{\prime }-{\mathrm e}^{y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ -{\mathrm e}^{-y} = x -1 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\ln \left (1-x \right ) \]

Problem 1895

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

Problem 1896

ODE	\[ \boxed {y^{2}-\frac {y^{\prime }}{x^{3} \left (x -1\right )}=-1} \] With initial conditions \begin {align*} [y \left (2\right ) = 0] \end {align*}
program solution	\[ y = \frac {-\cos \left (\frac {x^{4} \left (4 x -5\right )}{20}\right ) \tan \left (\frac {12}{5}\right )+\sin \left (\frac {x^{4} \left (4 x -5\right )}{20}\right )}{\sin \left (\frac {x^{4} \left (4 x -5\right )}{20}\right ) \tan \left (\frac {12}{5}\right )+\cos \left (\frac {x^{4} \left (4 x -5\right )}{20}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (\frac {1}{5} x^{5}-\frac {1}{4} x^{4}-\frac {12}{5}\right ) \]

Problem 1897

ODE	\[ \boxed {3 y^{\prime } x -y^{3}-2 y=-x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
program solution
Maple solution	\[ y \left (x \right ) = x^{\frac {2}{3}} \]

Problem 1898

ODE	\[ \boxed {\left (x^{2}+x +1\right ) y^{\prime }-y^{2}-2 y=5} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
program solution	N/A
Maple solution	\[ y \left (x \right ) = -1+2 \cot \left (\frac {4 \sqrt {3}\, \pi }{9}-\frac {4 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (2 x +1\right )}{3}\right )}{3}+\frac {\pi }{4}\right ) \]

Problem 1899

ODE	\[ \boxed {\left (x^{2}-2 x -8\right ) y^{\prime }-y^{2}-y=-2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
program solution	\[ y = \frac {-2 i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} x^{2}-2 \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}\, x^{2}-32 i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}}+16 \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}\, x +8 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}+2 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}\, x^{2}-32 \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}+16 i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} x +2 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} x^{2}+8 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}\, x +8 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} x +8 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}}}{i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} x^{2}+\left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}\, x^{2}+2 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}\, x^{2}-8 i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} x -8 \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}\, x +8 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}\, x +16 i \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}}+16 \left (\frac {2+x}{x -4}\right )^{\frac {5}{6}} \sqrt {3}+8 i \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} \sqrt {3}+2 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} x^{2}+8 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}} x +8 \sqrt {2}\, \left (\frac {x -4}{2+x}\right )^{\frac {2}{3}}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 x +8-2 \sqrt {-2 x^{2}+4 x +16}}{3 x +4} \]

Problem 1900

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