2.17.108 Problems 10701 to 10800

Problem 10701

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+A \sqrt {x}} \]
program solution
Maple solution	\[ \frac {196^{\frac {5}{6}} \left (\left (\frac {4 \left (x -\frac {7 y \left (x \right )}{4}\right ) \sqrt {3}\, \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {7}{6}\right ], \left [\frac {3}{2}\right ], \frac {3 \left (-4 x +7 y \left (x \right )\right )^{2}}{196 x^{\frac {3}{2}} A}\right )}{7}+\sqrt {x}\, \sqrt {A \sqrt {x}}\, c_{1} \right ) 196^{\frac {1}{6}} \left (\frac {A \,x^{\frac {3}{2}}-\frac {12 \left (x -\frac {7 y \left (x \right )}{4}\right )^{2}}{49}}{x^{\frac {3}{2}} A}\right )^{\frac {1}{6}}-7 \,14^{\frac {1}{3}} A \sqrt {3}\, \sqrt {x}\right )}{196 \left (\frac {A \,x^{\frac {3}{2}}-\frac {12 \left (x -\frac {7 y \left (x \right )}{4}\right )^{2}}{49}}{x^{\frac {3}{2}} A}\right )^{\frac {1}{6}} \sqrt {A \sqrt {x}}\, \sqrt {x}} = 0 \]

Problem 10702

ODE	\[ \boxed {y y^{\prime }-y=6 x +\frac {A}{x^{4}}} \]
program solution
Maple solution	\[ c_{1} +\frac {5 \,5^{\frac {2}{3}} \left (x +\frac {y \left (x \right )}{2}\right ) \left (x A 3^{\frac {5}{6}} \operatorname {hypergeom}\left (\left [\frac {1}{6}, \frac {2}{3}\right ], \left [\frac {5}{3}\right ], -\frac {2 A}{3 x^{3} \left (2 x +y \left (x \right )\right )^{2}}\right ) \left (\frac {12 x^{5}+12 y \left (x \right ) x^{4}+3 y \left (x \right )^{2} x^{3}+2 A}{x^{9} \left (2 x +y \left (x \right )\right )^{6}}\right )^{\frac {1}{6}}+\frac {24 \left (\frac {\left (-\frac {1}{x^{\frac {3}{2}} \left (2 x +y \left (x \right )\right )}\right )^{\frac {2}{3}} y \left (x \right )}{6}+\left (-\frac {1}{x^{\frac {3}{2}} \left (2 x +y \left (x \right )\right )}\right )^{\frac {5}{3}} x^{\frac {5}{2}} \left (x +\frac {y \left (x \right )}{2}\right )\right ) \left (6 x^{5}+6 y \left (x \right ) x^{4}+\frac {3 y \left (x \right )^{2} x^{3}}{2}+A \right )}{5}\right )}{2 \left (-\frac {1}{x^{\frac {3}{2}} \left (2 x +y \left (x \right )\right )}\right )^{\frac {7}{3}} x^{\frac {11}{2}} \left (\frac {12 x^{5}+12 y \left (x \right ) x^{4}+3 y \left (x \right )^{2} x^{3}+2 A}{x^{3} \left (2 x +y \left (x \right )\right )^{2}}\right )^{\frac {1}{6}} \left (2 x +y \left (x \right )\right )^{4}} = 0 \]

Problem 10703

ODE	\[ \boxed {y y^{\prime }-y=20 x +\frac {A}{\sqrt {x}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10704

ODE	\[ \boxed {y y^{\prime }-y=\frac {15 x}{4}+\frac {A}{x^{7}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10705

ODE	\[ \boxed {y y^{\prime }-y=-\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ c_{1} -\frac {\left (3 A +\sqrt {x}\right ) 2^{\frac {2}{3}} \left (\frac {3 A^{2}+16 A \sqrt {x}+5 x -7 y \left (x \right )}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}\right )^{\frac {5}{6}} y \left (x \right )}{2 \sqrt {\frac {\left (3 A +\sqrt {x}\right )^{2}}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}}\, \left (\frac {-24 A^{2}-2 A \sqrt {x}+2 x -7 y \left (x \right )}{6 A^{2}+2 A \sqrt {x}+y \left (x \right )}\right )^{\frac {1}{3}} \left (6 A^{2}+2 A \sqrt {x}+y \left (x \right )\right ) A}-\left (\int _{}^{\frac {6 A \sqrt {x}+2 x -3 y \left (x \right )}{12 A^{2}+4 A \sqrt {x}+2 y \left (x \right )}}\frac {\left (10 \textit {\_a} +1\right )^{\frac {5}{6}}}{\sqrt {2 \textit {\_a} +3}\, \left (\textit {\_a} -2\right )^{\frac {1}{3}}}d \textit {\_a} \right ) = 0 \]

Problem 10706

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49}} \]
program solution
Maple solution	\[ c_{1} +\frac {3 \sqrt {6}\, 4^{\frac {2}{3}} \left (\left (\sqrt {-35 A^{2}-7 A \sqrt {x}}\, \left (A \left (3+\frac {5 i \sqrt {6}}{3}\right ) \sqrt {x}+\frac {i \left (25 A^{2}+x \right ) \sqrt {6}}{6}-10 A^{2}+x -\frac {7 y \left (x \right )}{4}\right )-\frac {7 i x \sqrt {6}\, A}{6}+\left (-\frac {7 y \left (x \right )}{4}+5 A^{2}-\frac {35 i A^{2} \sqrt {6}}{3}\right ) \sqrt {x}-\frac {175 i A^{3} \sqrt {6}}{6}-50 A^{3}+\left (8 x -\frac {35 y \left (x \right )}{4}\right ) A +x^{\frac {3}{2}}\right ) \operatorname {hypergeom}\left (\left [-1, -\frac {1}{6}\right ], \left [\frac {2}{3}\right ], \frac {4 i \left (5 A +\sqrt {x}\right ) \sqrt {6}\, \sqrt {-35 A^{2}-7 A \sqrt {x}}}{10 i \sqrt {6}\, \left (A +\frac {\sqrt {x}}{5}\right ) \sqrt {-35 A^{2}-7 A \sqrt {x}}-120 A^{2}+36 A \sqrt {x}+12 x -21 y \left (x \right )}\right )+\frac {\sqrt {-35 A^{2}-7 A \sqrt {x}}\, \left (A \left (-7-5 i \sqrt {6}\right ) \sqrt {x}+\frac {i \left (-25 A^{2}-x \right ) \sqrt {6}}{2}-35 A^{2}\right )}{2}+\frac {175 \left (A +\frac {\sqrt {x}}{5}\right )^{2} A \left (i \sqrt {6}-2\right )}{4}\right )}{4 \left (\left (\left (2 \left (-18 i-7 \sqrt {6}\right ) A \sqrt {x}-70 A^{2} \sqrt {6}+120 i A^{2}-12 i x +21 i y \left (x \right )\right ) \sqrt {-35 A^{2}-7 A \sqrt {x}}+350 \left (-\frac {\sqrt {6}\, x}{25}+\frac {2 \left (-\sqrt {6}+\frac {9 i}{5}\right ) A \sqrt {x}}{5}-A^{2} \sqrt {6}-\frac {12 i A^{2}}{5}+\frac {6 i x}{25}-\frac {21 i y \left (x \right )}{50}\right ) A \right ) \operatorname {hypergeom}\left (\left [-\frac {2}{3}, \frac {1}{6}\right ], \left [\frac {4}{3}\right ], \frac {4 i \left (5 A +\sqrt {x}\right ) \sqrt {6}\, \sqrt {-35 A^{2}-7 A \sqrt {x}}}{10 i \sqrt {6}\, \left (A +\frac {\sqrt {x}}{5}\right ) \sqrt {-35 A^{2}-7 A \sqrt {x}}-120 A^{2}+36 A \sqrt {x}+12 x -21 y \left (x \right )}\right )+175 \left (\sqrt {-35 A^{2}-7 A \sqrt {x}}\, \left (\frac {A \sqrt {x}\, \left (\frac {6 i}{7}+\frac {\sqrt {6}}{5}\right )}{5}+\frac {A^{2} \sqrt {6}}{5}+\frac {3 i A^{2}}{7}+\frac {3 i x}{175}\right )+\left (\sqrt {6}-3 i\right ) \left (A +\frac {\sqrt {x}}{5}\right )^{2} A \right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}, \frac {7}{6}\right ], \left [\frac {7}{3}\right ], \frac {4 i \left (5 A +\sqrt {x}\right ) \sqrt {6}\, \sqrt {-35 A^{2}-7 A \sqrt {x}}}{10 i \sqrt {6}\, \left (A +\frac {\sqrt {x}}{5}\right ) \sqrt {-35 A^{2}-7 A \sqrt {x}}-120 A^{2}+36 A \sqrt {x}+12 x -21 y \left (x \right )}\right )\right ) {\left (\frac {i \left (5 A +\sqrt {x}\right ) \sqrt {6}\, \sqrt {-35 A^{2}-7 A \sqrt {x}}}{10 i \sqrt {6}\, \left (A +\frac {\sqrt {x}}{5}\right ) \sqrt {-35 A^{2}-7 A \sqrt {x}}-120 A^{2}+36 A \sqrt {x}+12 x -21 y \left (x \right )}\right )}^{\frac {1}{3}}} = 0 \]

Problem 10707

ODE	\[ \boxed {y y^{\prime }-y=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10708

ODE	\[ \boxed {y y^{\prime }-y=\frac {15 x}{4}+\frac {6 A}{x^{\frac {1}{3}}}-\frac {3 A^{2}}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10709

ODE	\[ \boxed {y y^{\prime }-y=-\frac {3 x}{16}+\frac {A}{x^{\frac {1}{3}}}+\frac {B}{x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10710

ODE	\[ \boxed {y y^{\prime }-y=-\frac {5 x}{36}+\frac {A}{x^{\frac {3}{5}}}-\frac {B}{x^{\frac {7}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10711

ODE	\[ \boxed {y y^{\prime }-y=\frac {k}{\sqrt {A \,x^{2}+B x +c}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10712

ODE	\[ \boxed {y y^{\prime }-y=-\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10713

ODE	\[ \boxed {y y^{\prime }-y=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{\frac {1}{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{\frac {1}{3}}}-\frac {A \,B^{3}}{x^{\frac {2}{3}}}\right )}{75}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10714

ODE	\[ \boxed {y y^{\prime }-y=\frac {3 x}{4}-\frac {3 A \,x^{\frac {1}{3}}}{2}+\frac {3 A^{2}}{4 x^{\frac {1}{3}}}-\frac {27 A^{4}}{625 x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10715

ODE	\[ \boxed {y y^{\prime }-y=-\frac {6 x}{25}+\frac {7 A \,x^{\frac {1}{3}}}{5}+\frac {31 A^{2}}{3 x^{\frac {1}{3}}}-\frac {100 A^{4}}{3 x^{\frac {5}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10716

ODE	\[ \boxed {y y^{\prime }-y=-\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{\frac {1}{5}}}-\frac {7 A^{3}}{20 x^{\frac {4}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10717

ODE	\[ \boxed {y y^{\prime }-y=-\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{\frac {5}{11}}}-\frac {770 A^{3}}{9 x^{\frac {13}{11}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10718

ODE	\[ \boxed {y y^{\prime }-y=-\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{\frac {1}{7}}}+\frac {280 A}{x^{\frac {5}{7}}}-\frac {400 A^{2}}{x^{\frac {9}{7}}}\right )}{9}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10719

ODE	\[ \boxed {y y^{\prime }-y=a x +b \,x^{m}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10720

ODE	\[ \boxed {y y^{\prime }-y=-\frac {\left (1+m \right ) x}{\left (2+m \right )^{2}}+A \,x^{1+2 m}+B \,x^{3 m +1}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10721

ODE	\[ \boxed {y y^{\prime }-y=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (\lambda b +1\right ) {\mathrm e}^{\lambda x}+b} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10722

ODE	\[ \boxed {y y^{\prime }-y=a^{2} \lambda \,{\mathrm e}^{2 \lambda x}+{\mathrm e}^{\lambda x} a \lambda x +b \,{\mathrm e}^{\lambda x}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10723

ODE	\[ \boxed {y y^{\prime }-y=2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 a \sin \left (\lambda x \right )} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10724

ODE	\[ \boxed {y y^{\prime }-y=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10725

ODE	\[ \boxed {y y^{\prime }-\left (a x +b \right ) y=1} \]
program solution
Maple solution	\[ \frac {\left (a x +b \right ) \left (\operatorname {AiryBi}\left (-\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right ) c_{1} -\operatorname {AiryAi}\left (-\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right )\right ) \left (-a^{2}\right )^{\frac {1}{3}} 2^{\frac {1}{3}}+2 \left (\operatorname {AiryBi}\left (1, -\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right ) c_{1} -\operatorname {AiryAi}\left (1, -\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right )\right ) a}{2^{\frac {1}{3}} \left (-a^{2}\right )^{\frac {1}{3}} \left (a x +b \right ) \operatorname {AiryBi}\left (-\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right )+2 \operatorname {AiryBi}\left (1, -\frac {\left (-2 a y \left (x \right )+\left (a x +b \right )^{2}\right ) 2^{\frac {2}{3}}}{4 \left (-a^{2}\right )^{\frac {1}{3}}}\right ) a} = 0 \]

Problem 10726

ODE	\[ \boxed {y y^{\prime }-\frac {y}{\left (a x +b \right )^{2}}=1} \]
program solution
Maple solution	\[ \frac {-a \left (-\operatorname {AiryBi}\left (-\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right ) c_{1} +\operatorname {AiryAi}\left (-\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right )\right ) \left (1+a \left (a x +b \right ) y \left (x \right )\right ) 2^{\frac {1}{3}}+2 \left (a x +b \right ) \left (a^{2}\right )^{\frac {2}{3}} \left (\operatorname {AiryBi}\left (1, -\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right ) c_{1} -\operatorname {AiryAi}\left (1, -\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right )\right )}{a 2^{\frac {1}{3}} \left (1+a \left (a x +b \right ) y \left (x \right )\right ) \operatorname {AiryBi}\left (-\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right )+2 \operatorname {AiryBi}\left (1, -\frac {2^{\frac {2}{3}} \left (-\frac {a^{2} \left (a x +b \right )^{2} y \left (x \right )^{2}}{2}+\left (-a^{2} x -a b \right ) y \left (x \right )+a^{4} x^{3}+3 a^{3} b \,x^{2}+3 a^{2} b^{2} x +a \,b^{3}-\frac {1}{2}\right )}{2 \left (a^{2}\right )^{\frac {1}{3}} \left (a x +b \right )^{2}}\right ) \left (a^{2}\right )^{\frac {2}{3}} \left (a x +b \right )} = 0 \]

Problem 10727

ODE	\[ \boxed {y y^{\prime }-\left (a -\frac {1}{a x}\right ) y=1} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {a^{2} x -\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}}-\operatorname {expIntegral}_{1}\left (-\textit {\_Z} \right ) a^{2} x +c_{1} a^{2} x \right )}{a} \]

Problem 10728

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

Problem 10729

ODE	\[ \boxed {y y^{\prime }-\frac {3 y}{\sqrt {a \,x^{\frac {3}{2}}+8 x}}=1} \]
program solution
Maple solution	\[ \frac {{\left (-\frac {a \sqrt {x}\, \left (-2 a \,x^{\frac {3}{2}}+\sqrt {x}\, a y \left (x \right )^{2}-8 \sqrt {x \left (8+\sqrt {x}\, a \right )}\, y \left (x \right )-16 x \right )}{\left (\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}\right )^{2}}\right )}^{\frac {1}{4}} \sqrt {2 \sqrt {x}\, a +16}\, a \sqrt {x}\, y \left (x \right )+4 \sqrt {-\frac {\sqrt {2 \sqrt {x}\, a +16}\, \sqrt {x \left (8+\sqrt {x}\, a \right )}}{\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}}}\, \left (\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}\right ) \left (\int _{}^{-\frac {\sqrt {2 \sqrt {x}\, a +16}\, \sqrt {x \left (8+\sqrt {x}\, a \right )}}{\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}}}\frac {\left (\textit {\_a}^{2}-1\right )^{\frac {1}{4}}}{\sqrt {\textit {\_a}}}d \textit {\_a} +\frac {c_{1}}{4}\right )}{\sqrt {-\frac {\sqrt {2 \sqrt {x}\, a +16}\, \sqrt {x \left (8+\sqrt {x}\, a \right )}}{\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}}}\, \left (\sqrt {x}\, a y \left (x \right )-4 \sqrt {x \left (8+\sqrt {x}\, a \right )}\right )} = 0 \]

Problem 10730

ODE	\[ \boxed {y y^{\prime }-\left (\frac {a}{x^{\frac {2}{3}}}-\frac {2}{3 a \,x^{\frac {1}{3}}}\right ) y=1} \]
program solution
Maple solution	\[ \frac {-\sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}\, \operatorname {BesselI}\left (1, \frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right ) c_{1} a^{2}+\operatorname {BesselK}\left (1, -\frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right ) \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}\, a^{2}+x^{\frac {1}{3}} \operatorname {BesselI}\left (0, \frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right ) c_{1} -x^{\frac {1}{3}} \operatorname {BesselK}\left (0, -\frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right )}{-\operatorname {BesselI}\left (1, \frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right ) \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}\, a^{2}+x^{\frac {1}{3}} \operatorname {BesselI}\left (0, \frac {2 \sqrt {\frac {x^{\frac {2}{3}}+a y \left (x \right )}{a^{4}}}}{3}\right )} = 0 \]

Problem 10731

ODE	\[ \boxed {y y^{\prime }-{\mathrm e}^{\lambda x} y a=1} \]
program solution
Maple solution	\[ c_{1} +a \,\operatorname {erf}\left (\frac {\left (\lambda y \left (x \right )-{\mathrm e}^{x \lambda } a \right ) \sqrt {2}}{2 \sqrt {-\lambda }}\right ) \sqrt {2}\, \sqrt {\pi }-2 \sqrt {-\lambda }\, {\mathrm e}^{\frac {y \left (x \right )^{2} \lambda ^{2}-2 y \left (x \right ) {\mathrm e}^{x \lambda } a \lambda +a^{2} {\mathrm e}^{2 x \lambda }-2 x \,\lambda ^{2}}{2 \lambda }} = 0 \]

Problem 10732

ODE	\[ \boxed {y y^{\prime }-\left (a \,{\mathrm e}^{\lambda x}+{\mathrm e}^{-\lambda x} b \right ) y=1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10733

ODE	\[ \boxed {y y^{\prime }-a y \cosh \left (x \right )=1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10734

ODE	\[ \boxed {y y^{\prime }-a y \sinh \left (x \right )=1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10735

ODE	\[ \boxed {y y^{\prime }-a \cos \left (\lambda x \right ) y=1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10736

ODE	\[ \boxed {y y^{\prime }-a \sin \left (\lambda x \right ) y=1} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10737

ODE	\[ \boxed {y y^{\prime }-\left (a x +3 b \right ) y=-a b \,x^{2}+c \,x^{3}-2 b^{2} x} \]
program solution
Maple solution	\[ \frac {x \left (\frac {-2 y \left (x \right )^{2}+x \left (a x +4 b \right ) y \left (x \right )-a b \,x^{3}+c \,x^{4}-2 b^{2} x^{2}}{\left (b x -y \left (x \right )\right )^{2}}\right )^{\frac {1}{4}} {\mathrm e}^{-\frac {a \,\operatorname {arctanh}\left (\frac {-a b x +2 c \,x^{2}+a y \left (x \right )}{\left (-b x +y \left (x \right )\right ) \sqrt {a^{2}+8 c}}\right )}{2 \sqrt {a^{2}+8 c}}} y \left (x \right )+\sqrt {\frac {x^{2}}{-b x +y \left (x \right )}}\, \left (b x -y \left (x \right )\right ) \left (\left (\int _{}^{\frac {x^{2}}{-b x +y \left (x \right )}}\frac {\left (\textit {\_a}^{2} c +a \textit {\_a} -2\right )^{\frac {1}{4}} {\mathrm e}^{-\frac {a \,\operatorname {arctanh}\left (\frac {2 c \textit {\_a} +a}{\sqrt {a^{2}+8 c}}\right )}{2 \sqrt {a^{2}+8 c}}}}{\sqrt {\textit {\_a}}}d \textit {\_a} \right ) b +c_{1} \right )}{\sqrt {\frac {x^{2}}{-b x +y \left (x \right )}}\, \left (b x -y \left (x \right )\right )} = 0 \]

Problem 10738

ODE	\[ \boxed {y y^{\prime }-\left (3 a x +b \right ) y=-a^{2} x^{3}-a b \,x^{2}+c x} \]
program solution	\[ \frac {a \left (\ln \left (a^{2} x^{4}+a b \,x^{3}+\left (-2 a y-c \right ) x^{2}-y b x +y^{2}\right ) \sqrt {b^{2}+4 c}+2 b \,\operatorname {arctanh}\left (\frac {2 a \,x^{2}+b x -2 y}{x \sqrt {b^{2}+4 c}}\right )-2 \ln \left (-a^{2} x^{2}+\left (-b x +y\right ) a +c \right ) \sqrt {b^{2}+4 c}\right )}{2 \sqrt {b^{2}+4 c}\, c} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {9 x \left (b^{2}+3 c \right ) \left (a^{2} x^{2}+a b x -c \right )}{-b \,{\mathrm e}^{\operatorname {RootOf}\left (2 a \,b^{8} \operatorname {arctanh}\left (\frac {b^{2} \left (9 b^{2}+27 c +2 \,{\mathrm e}^{\textit {\_Z}}\right )}{9 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}}\right )+20 a \,b^{6} c \,\operatorname {arctanh}\left (\frac {b^{2} \left (9 b^{2}+27 c +2 \,{\mathrm e}^{\textit {\_Z}}\right )}{9 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}}\right )+66 a \,b^{4} c^{2} \operatorname {arctanh}\left (\frac {b^{2} \left (9 b^{2}+27 c +2 \,{\mathrm e}^{\textit {\_Z}}\right )}{9 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}}\right )+72 a \,b^{2} c^{3} \operatorname {arctanh}\left (\frac {b^{2} \left (9 b^{2}+27 c +2 \,{\mathrm e}^{\textit {\_Z}}\right )}{9 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}}\right )+\sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \ln \left (-\frac {\left (2 b^{2}+9 c \right ) \left (a^{2} x^{2}+a b x -c \right )}{x^{2} \left (81 b^{4} c -9 b^{4} {\mathrm e}^{\textit {\_Z}}+486 b^{2} c^{2}-27 b^{2} c \,{\mathrm e}^{\textit {\_Z}}-b^{2} {\mathrm e}^{2 \textit {\_Z}}+729 c^{3}\right )}\right ) a \,b^{4}+2 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \textit {\_Z} a \,b^{4}-2 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \sqrt {a^{2} \left (b^{2}+4 c \right )}\, b^{3} \operatorname {arctanh}\left (\frac {a \left (2 a x +b \right )}{\sqrt {a^{2} \left (b^{2}+4 c \right )}}\right )+7 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \ln \left (-\frac {\left (2 b^{2}+9 c \right ) \left (a^{2} x^{2}+a b x -c \right )}{x^{2} \left (81 b^{4} c -9 b^{4} {\mathrm e}^{\textit {\_Z}}+486 b^{2} c^{2}-27 b^{2} c \,{\mathrm e}^{\textit {\_Z}}-b^{2} {\mathrm e}^{2 \textit {\_Z}}+729 c^{3}\right )}\right ) a \,b^{2} c +6 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, c_{1} a \,b^{2} c +14 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \textit {\_Z} a \,b^{2} c -6 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \sqrt {a^{2} \left (b^{2}+4 c \right )}\, b c \,\operatorname {arctanh}\left (\frac {a \left (2 a x +b \right )}{\sqrt {a^{2} \left (b^{2}+4 c \right )}}\right )+12 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \ln \left (-\frac {\left (2 b^{2}+9 c \right ) \left (a^{2} x^{2}+a b x -c \right )}{x^{2} \left (81 b^{4} c -9 b^{4} {\mathrm e}^{\textit {\_Z}}+486 b^{2} c^{2}-27 b^{2} c \,{\mathrm e}^{\textit {\_Z}}-b^{2} {\mathrm e}^{2 \textit {\_Z}}+729 c^{3}\right )}\right ) a \,c^{2}+24 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, c_{1} a \,c^{2}+24 \sqrt {b^{2} \left (b^{2}+4 c \right ) \left (b^{2}+3 c \right )^{2}}\, \textit {\_Z} a \,c^{2}\right )}+9 a x \left (b^{2}+3 c \right )} \]

Problem 10739

ODE	\[ \boxed {2 y y^{\prime }-\left (7 a x +5 b \right ) y=-3 a^{2} x^{3}-3 b^{2} x -2 c \,x^{2}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10740

ODE	\[ \boxed {y y^{\prime }-\left (\left (3-m \right ) x -1\right ) y=-\left (m -1\right ) a x} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10741

ODE	\[ \boxed {y y^{\prime }+x \left (a \,x^{2}+b \right ) y=-x} \]
program solution
Maple solution	\[ \frac {2 \operatorname {AiryBi}\left (1, \frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right ) a^{\frac {1}{3}} c_{1} +c_{1} \left (a \,x^{2}+b \right ) \operatorname {AiryBi}\left (\frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right )-2 \operatorname {AiryAi}\left (1, \frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right ) a^{\frac {1}{3}}-\left (a \,x^{2}+b \right ) \operatorname {AiryAi}\left (\frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right )}{2 \operatorname {AiryBi}\left (1, \frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right ) a^{\frac {1}{3}}+\operatorname {AiryBi}\left (\frac {4 a y \left (x \right )+\left (a \,x^{2}+b \right )^{2}}{4 a^{\frac {2}{3}}}\right ) \left (a \,x^{2}+b \right )} = 0 \]

Problem 10742

ODE	\[ \boxed {y y^{\prime }+a \left (1-\frac {1}{x}\right ) y=a^{2}} \]
program solution
Maple solution	\[ y \left (x \right ) = a \left (-x +\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}}-\operatorname {expIntegral}_{1}\left (-\textit {\_Z} \right ) x +c_{1} x \right )\right ) \]

Problem 10743

ODE	\[ \boxed {y y^{\prime }-a \left (1-\frac {b}{x}\right ) y=a^{2} b} \]
program solution
Maple solution	\[ y \left (x \right ) = a \left (-\operatorname {RootOf}\left (-{\mathrm e}^{\textit {\_Z}} b -\operatorname {expIntegral}_{1}\left (-\textit {\_Z} \right ) x +c_{1} x \right ) b +x \right ) \]

Problem 10744

ODE	\[ \boxed {y y^{\prime }-x^{n -1} \left (\left (1+2 n \right ) x +n a \right ) y=-n \,x^{2 n} \left (x +a \right )} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {2 \left (-\frac {\sqrt {-n^{2}}\, x \tan \left (\frac {\operatorname {RootOf}\left (-2 a n \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-n x \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-\tan \left (\frac {\textit {\_a} \sqrt {-n^{2}}}{2}\right ) \textit {\_Z} \sqrt {-n^{2}}\, x +2 c_{1} x \,{\mathrm e}^{\textit {\_a}}\right ) \sqrt {-n^{2}}}{2}\right )}{2}+n \left (a +\frac {x}{2}\right )\right ) x^{n}}{\tan \left (\frac {\operatorname {RootOf}\left (-2 a n \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-n x \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-\tan \left (\frac {\textit {\_a} \sqrt {-n^{2}}}{2}\right ) \textit {\_Z} \sqrt {-n^{2}}\, x +2 c_{1} x \,{\mathrm e}^{\textit {\_a}}\right ) \sqrt {-n^{2}}}{2}\right ) \sqrt {-n^{2}}-n} \]

Problem 10745

ODE	\[ \boxed {y y^{\prime }-a \left (-b n +x \right ) x^{n -1} y=c \left (x^{2}-\left (1+2 n \right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10746

ODE	\[ \boxed {y y^{\prime }-\left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y=\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{2 n -1}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10747

ODE	\[ \boxed {y y^{\prime }-\left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y=-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10748

ODE	\[ \boxed {y y^{\prime }-\frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}=\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10749

ODE	\[ \boxed {y y^{\prime }-\left (a \left (1+2 n \right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{-2+n} y=-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10750

ODE	\[ \boxed {y y^{\prime }-\left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y=-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10751

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x}=\frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x}} \]
program solution
Maple solution	\[ -\frac {27 \left (m -1\right ) \left (-54 m^{4} x a \left (m +2\right ) \left (m +\frac {1}{2}\right ) \left (\int _{}^{\frac {9 m \left (\left (m -1\right ) y \left (x \right )+3 \left (\frac {1}{3}+\left (x -\frac {1}{3}\right ) m \right ) a \right )}{\left (m -1\right ) \left (1+2 m \right ) \left (m +2\right ) \left (-y \left (x \right )+a \right )}}\frac {\textit {\_a} {\left (\left (m^{2}+m -2\right ) \textit {\_a} -9 m \right )}^{\frac {1}{1+m}} {\left (\left (2 m^{2}-m -1\right ) \textit {\_a} +9 m \right )}^{\frac {m}{1+m}}}{8 \left (\left (m^{2}-\frac {1}{2} m -\frac {1}{2}\right ) \textit {\_a} +\frac {9 m}{2}\right ) \left (\left (m^{2}+m -2\right ) \textit {\_a} -9 m \right ) {\left (\left (m^{2}+\frac {5}{2} m +1\right ) \textit {\_a} +\frac {9 m}{2}\right )}^{2}}d \textit {\_a} \right )+\left (-y \left (x \right )+a \right ) \left (\frac {1}{3}+\left (x -\frac {1}{3}\right ) m \right ) \left (\frac {\left (\left (-1+x \right ) a +y \left (x \right )\right ) m^{2}}{\left (1+2 m \right ) \left (-y \left (x \right )+a \right )}\right )^{\frac {1}{1+m}} \left (\frac {\left (a m x +a -y \left (x \right )\right ) m}{\left (m +2\right ) \left (-y \left (x \right )+a \right )}\right )^{\frac {m}{1+m}}-\frac {2 m x c_{1} a \left (m +2\right ) \left (m +\frac {1}{2}\right )}{27}\right )}{m \left (2 m^{3}+3 m^{2}-3 m -2\right ) a x} = 0 \]

Problem 10752

ODE	\[ \boxed {y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y=\frac {a^{2} b}{\sqrt {x}}} \]
program solution
Maple solution	\[ \frac {\left (b^{2}\right )^{\frac {1}{3}} c_{1} 2^{\frac {2}{3}} \left (-\sqrt {x}+b \right ) \operatorname {AiryBi}\left (\frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right )+2 \operatorname {AiryBi}\left (1, \frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right ) c_{1} b -2 \operatorname {AiryAi}\left (1, \frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right ) b -\left (b^{2}\right )^{\frac {1}{3}} 2^{\frac {2}{3}} \left (-\sqrt {x}+b \right ) \operatorname {AiryAi}\left (\frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right )}{\left (b^{2}\right )^{\frac {1}{3}} 2^{\frac {2}{3}} \left (-\sqrt {x}+b \right ) \operatorname {AiryBi}\left (\frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right )+2 \operatorname {AiryBi}\left (1, \frac {2^{\frac {1}{3}} \left (-2 \sqrt {x}\, a b +\left (b^{2}+x \right ) a -y \left (x \right )\right )}{2 \left (b^{2}\right )^{\frac {1}{3}} a}\right ) b} = 0 \]

Problem 10753

ODE	\[ \boxed {y y^{\prime }-\frac {3 y}{\left (a x +b \right )^{\frac {1}{3}} x^{\frac {5}{3}}}=\frac {3}{\left (a x +b \right )^{\frac {2}{3}} x^{\frac {7}{3}}}} \]
program solution
Maple solution	\[ y \left (x \right ) = -\frac {6 \sqrt {3}}{\left (a x +b \right )^{\frac {1}{3}} x^{\frac {2}{3}} \left (\left (\left (a x +b \right )^{\frac {1}{3}} x^{\frac {5}{3}} \left (\frac {a}{\left (a x +b \right )^{2} x^{4}}\right )^{\frac {1}{3}}+2\right ) \sqrt {3}+3 x^{\frac {5}{3}} \left (a x +b \right )^{\frac {1}{3}} \left (\frac {a}{\left (a x +b \right )^{2} x^{4}}\right )^{\frac {1}{3}} \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (\frac {\tan \left (\textit {\_Z} \right )^{2}+1}{\left (\sqrt {3}+\tan \left (\textit {\_Z} \right )\right )^{2}}\right )+6 \sqrt {3}\, c_{1} -2 \sqrt {3}\, \left (\int \left (\frac {a}{\left (a x +b \right )^{2} x^{4}}\right )^{\frac {2}{3}} \left (a x +b \right )^{\frac {2}{3}} x^{\frac {7}{3}}d x \right )-6 \textit {\_Z} \right )\right )\right )} \]

Problem 10754

ODE	\[ \boxed {3 y y^{\prime }-\frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{\frac {1}{3}}}=\frac {6 \lambda s x -6}{x^{\frac {2}{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{\frac {1}{3}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10755

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x}=-\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x}} \]
program solution
Maple solution	\[ c_{1} +\frac {\sqrt {2}\, \left (\frac {i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}}{x a}\right )^{\frac {3}{2}} \left (-\frac {i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}\, \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {3}{2}\right ], \left [\frac {7}{2}\right ], \frac {i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}}{2 x a}\right )}{8 x a}+\frac {5 \left (4 i \sqrt {2}\, x -i \sqrt {2}-6 i \sqrt {-x}+4 x +2\right ) \operatorname {hypergeom}\left (\left [-\frac {1}{2}, \frac {1}{2}\right ], \left [\frac {5}{2}\right ], \frac {i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}}{2 x a}\right )}{4 \left (4 i \sqrt {2}\, x +i \sqrt {2}-2 i \sqrt {-x}-4 \sqrt {2}\, \sqrt {-x}+4 x -2\right )}\right )}{2 \left (\frac {3}{2}-\frac {4 i \sqrt {2}\, x -i \sqrt {2}-6 i \sqrt {-x}+4 x +2}{2 \left (4 i \sqrt {2}\, x +i \sqrt {2}-2 i \sqrt {-x}-4 \sqrt {2}\, \sqrt {-x}+4 x -2\right )}\right ) \operatorname {hypergeom}\left (\left [-2, -1\right ], \left [-\frac {1}{2}\right ], \frac {i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}}{2 x a}\right )+\frac {4 i \left (i \sqrt {-x}\, a +2 a x +y \left (x \right )-a \right ) \sqrt {-x}}{x a}} = 0 \]

Problem 10756

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2}=\frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10757

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{\frac {9}{7}}}=-\frac {3 a^{2} \left (x -1\right ) \left (x -8\right )}{14 x^{\frac {11}{17}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10758

ODE	\[ \boxed {y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{\frac {9}{7}}}=-\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{\frac {11}{17}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10759

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{\frac {18}{13}}}=-\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{\frac {23}{13}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10760

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{\frac {7}{5}}}=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10761

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}=a^{2} \left (-x^{2}+1\right )} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10762

ODE	\[ \boxed {y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{\frac {7}{5}} y}{35}=-\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{\frac {9}{5}}}{35}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10763

ODE	\[ \boxed {y y^{\prime }+\frac {3 a \left (3 x +7\right ) y}{10 x^{\frac {13}{10}}}=-\frac {a^{2} \left (x -1\right ) \left (x +9\right )}{5 x^{\frac {8}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10764

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{\frac {7}{5}}}=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10765

ODE	\[ \boxed {y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{\frac {7}{5}}}=-\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10766

ODE	\[ \boxed {y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{\frac {10}{7}}}=-\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{\frac {13}{7}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10767

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{\frac {7}{4}}}=\frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{\frac {5}{2}}}} \]
program solution
Maple solution	\[ \frac {\frac {36 \sqrt {-\frac {\left (-1+x \right ) a +x^{\frac {3}{4}} y \left (x \right )}{x^{\frac {3}{4}} \left (y \left (x \right )+x^{\frac {1}{4}} a \right )}}\, \sqrt {13}\, 55^{\frac {1}{6}} \left (x -\frac {15}{2}\right ) \left (\frac {\left (3 x +5\right ) a +3 x^{\frac {3}{4}} y \left (x \right )}{x^{\frac {3}{4}} \left (y \left (x \right )+x^{\frac {1}{4}} a \right )}\right )^{\frac {5}{6}}}{20449}+1458000 \left (\int _{}^{-\frac {90 \left (2 x^{\frac {3}{4}} y \left (x \right )+2 a x -15 a \right )}{143 \left (x^{\frac {3}{4}} y \left (x \right )+a x \right )}}\frac {\textit {\_a} \sqrt {11 \textit {\_a} -90}\, \left (13 \textit {\_a} +90\right )^{\frac {5}{6}}}{\left (143 \textit {\_a} +180\right )^{\frac {4}{3}} \left (20449 \textit {\_a}^{3}-1190700 \textit {\_a} -1458000\right )}d \textit {\_a} +\frac {c_{1}}{1458000}\right ) \left (\frac {a}{x^{\frac {3}{4}} \left (y \left (x \right )+x^{\frac {1}{4}} a \right )}\right )^{\frac {4}{3}} x}{\left (\frac {a}{x^{\frac {3}{4}} \left (y \left (x \right )+x^{\frac {1}{4}} a \right )}\right )^{\frac {4}{3}} x} = 0 \]

Problem 10768

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{\frac {7}{4}}}=\frac {a^{2} \left (x -1\right ) \left (x +5\right )}{4 x^{\frac {5}{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10769

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{\frac {8}{7}}}=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{\frac {9}{7}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10770

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{\frac {2}{3}}}=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{\frac {1}{3}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10771

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{\frac {8}{7}}}=\frac {a^{2} \left (x -1\right ) \left (32 x +3\right )}{28 x^{\frac {9}{7}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10772

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}} \]
program solution
Maple solution	\[ c_{1} -\frac {9 \,2^{\frac {2}{3}} \sqrt {\frac {x^{3} y \left (x \right )+a x -a}{\left (y \left (x \right ) x^{2}+a \right ) x}}\, \left (x -\frac {3}{4}\right ) 5^{\frac {1}{6}}}{5 x {\left (-\frac {a}{\left (y \left (x \right ) x^{2}+a \right ) x}\right )}^{\frac {1}{3}} \left (\frac {3 x^{3} y \left (x \right )+3 a x -a}{\left (y \left (x \right ) x^{2}+a \right ) x}\right )^{\frac {1}{6}}}-729 \left (\int _{}^{\frac {\frac {9 x^{3} y \left (x \right )}{5}+\frac {9 a x}{5}-\frac {27 a}{20}}{\left (y \left (x \right ) x^{2}+a \right ) x}}\frac {\textit {\_a} \sqrt {20 \textit {\_a} -9}}{\left (5 \textit {\_a} -9\right )^{\frac {1}{3}} \left (9+4 \textit {\_a} \right )^{\frac {1}{6}} \left (400 \textit {\_a}^{3}-1701 \textit {\_a} +729\right )}d \textit {\_a} \right ) = 0 \]

Problem 10773

ODE	\[ \boxed {y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10774

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{\frac {9}{7}}}=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{\frac {11}{7}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10775

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (x -2\right ) y}{x}=\frac {2 a^{2} \left (x -1\right )}{x}} \]
program solution
Maple solution	\[ \frac {\sqrt {\frac {\left (1-x \right ) a -y \left (x \right )}{a x +y \left (x \right )}}\, {\mathrm e}^{\frac {a x +y \left (x \right )}{2 a}} y \left (x \right )+x \left (\int _{}^{\frac {a}{a x +y \left (x \right )}}\frac {\sqrt {\textit {\_a} -1}\, {\mathrm e}^{\frac {1}{2 \textit {\_a}}}}{\sqrt {\textit {\_a}}}d \textit {\_a} +c_{1} \right ) \sqrt {\frac {a}{a x +y \left (x \right )}}\, \left (a x +y \left (x \right )\right )}{\sqrt {\frac {a}{a x +y \left (x \right )}}\, x \left (a x +y \left (x \right )\right )} = 0 \]

Problem 10776

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x}=-\frac {2 a^{2} \left (x -1\right )^{2}}{x}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10777

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}=\frac {a^{2} b}{x}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10778

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{\frac {5}{2}}}=\frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10779

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{\frac {6}{5}}}=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{\frac {7}{5}}}} \]
program solution
Maple solution	\[ \text {Expression too large to display} \]

Problem 10780

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{\frac {5}{2}}}=-\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10781

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{\frac {22}{15}}}=-\frac {a^{2} \left (x -1\right ) \left (x +4\right )}{30 x^{\frac {29}{15}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10782

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{\frac {5}{2}}}=-\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10783

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (24 x +11\right ) x^{\frac {27}{20}} y}{30}=-\frac {a^{2} \left (x -1\right ) \left (9 x +1\right )}{60 x^{\frac {17}{10}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10784

ODE	\[ \boxed {y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{\frac {8}{5}}}=\frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{\frac {11}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10785

ODE	\[ \boxed {y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{\frac {7}{5}}}=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10786

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{\frac {8}{5}}}=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{\frac {3}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10787

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{\frac {8}{5}}}=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{\frac {11}{5}}}} \]
program solution
Maple solution	\[ \frac {\frac {360 \,2^{\frac {1}{3}} \sqrt {17}\, \sqrt {-\frac {\left (-1+x \right ) a +y \left (x \right ) x^{\frac {3}{5}}}{x^{\frac {3}{5}} \left (y \left (x \right )+a \,x^{\frac {2}{5}}\right )}}\, 91^{\frac {5}{6}} \left (x -\frac {21}{4}\right ) \left (\frac {\left (3 x +7\right ) a +3 y \left (x \right ) x^{\frac {3}{5}}}{x^{\frac {3}{5}} \left (y \left (x \right )+a \,x^{\frac {2}{5}}\right )}\right )^{\frac {7}{6}}}{4444531}[phone] x \left (\int _{}^{-\frac {315 \left (4 y \left (x \right ) x^{\frac {3}{5}}+4 a x -21 a \right )}{884 \left (y \left (x \right ) x^{\frac {3}{5}}+a x \right )}}\frac {\sqrt {52 \textit {\_a} -315}\, \left (68 \textit {\_a} +315\right )^{\frac {1}{6}} \textit {\_a}}{\left (11492 \textit {\_a}^{2}-53235 \textit {\_a} -99225\right ) \left (221 \textit {\_a} +315\right )^{\frac {5}{3}}}d \textit {\_a} +\frac {c_{1}}{31255875}\right ) \left (\frac {a}{x^{\frac {3}{5}} \left (y \left (x \right )+a \,x^{\frac {2}{5}}\right )}\right )^{\frac {5}{3}}}{x \left (\frac {a}{x^{\frac {3}{5}} \left (y \left (x \right )+a \,x^{\frac {2}{5}}\right )}\right )^{\frac {5}{3}}} = 0 \]

Problem 10788

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{\frac {5}{2}}}=\frac {a^{2} \left (x -1\right ) \left (3 x +1\right )}{2 x^{4}}} \]
program solution
Maple solution	\[ \frac {\frac {18 \sqrt {\frac {\left (-1+x \right ) a +y \left (x \right ) x^{\frac {3}{2}}}{x \left (y \left (x \right ) \sqrt {x}+a \right )}}\, \sqrt {5}\, 7^{\frac {5}{6}} \left (x +\frac {3}{2}\right ) \left (\frac {\left (-3 x -1\right ) a -3 y \left (x \right ) x^{\frac {3}{2}}}{x \left (y \left (x \right ) \sqrt {x}+a \right )}\right )^{\frac {1}{6}}}{1225}+1458 \left (\int _{}^{\frac {-\frac {18 y \left (x \right ) x^{\frac {3}{2}}}{35}+\frac {9 \left (-2 x -3\right ) a}{35}}{x \left (y \left (x \right ) \sqrt {x}+a \right )}}\frac {\textit {\_a} \left (5 \textit {\_a} -9\right )^{\frac {1}{6}} \sqrt {7 \textit {\_a} +9}}{\left (35 \textit {\_a} +18\right )^{\frac {2}{3}} \left (1225 \textit {\_a}^{3}-3159 \textit {\_a} -1458\right )}d \textit {\_a} +\frac {c_{1}}{1458}\right ) x \left (-\frac {a}{x \left (y \left (x \right ) \sqrt {x}+a \right )}\right )^{\frac {2}{3}}}{x \left (-\frac {a}{x \left (y \left (x \right ) \sqrt {x}+a \right )}\right )^{\frac {2}{3}}} = 0 \]

Problem 10789

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{\frac {7}{5}}}=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ c_{1} -\frac {80 \sqrt {3}\, \left (a y \left (x \right ) x^{\frac {2}{5}}+\frac {x^{\frac {4}{5}} y \left (x \right )^{2}}{8}+\frac {\left (y \left (x \right ) x^{\frac {7}{5}}-2 a \left (x +24\right ) \left (-1+x \right )\right ) a}{24}\right ) \left (a y \left (x \right ) x^{\frac {2}{5}}+\frac {x^{\frac {4}{5}} y \left (x \right )^{2}}{8}+\frac {a \left (y \left (x \right ) x^{\frac {7}{5}}+\frac {a \left (x +4\right )^{2}}{2}\right )}{4}\right ) \sqrt {\frac {-y \left (x \right ) x^{\frac {2}{5}}-a x +a}{x^{\frac {2}{5}} \left (y \left (x \right )+x^{\frac {3}{5}} a \right )}}}{9 \left (\frac {a}{x^{\frac {2}{5}} \left (y \left (x \right )+x^{\frac {3}{5}} a \right )}\right )^{\frac {5}{2}} \left (a \left (x +4\right )+y \left (x \right ) x^{\frac {2}{5}}\right )^{2} \left (y \left (x \right ) x^{\frac {2}{5}}+a x \right )^{2} x} = 0 \]

Problem 10790

ODE	\[ \boxed {y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{\frac {7}{5}}}=-\frac {2 a^{2} \left (x -1\right ) \left (9 x -4\right )}{5 x^{\frac {9}{5}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10791

ODE	\[ \boxed {y y^{\prime }-\frac {3 a y}{x^{\frac {7}{4}}}=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{\frac {5}{2}}}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10792

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}}=\frac {a^{2} \left (k +1\right ) \left (x -1\right )}{x^{2}}} \]
program solution
Maple solution	\[ \frac {\left (\frac {a x}{-y \left (x \right ) x +a}\right )^{-\frac {1}{1+k}} x^{2} \left (\frac {\left (-1+x \right ) a +y \left (x \right ) x}{-y \left (x \right ) x +a}\right )^{\frac {1}{1+k}} {\mathrm e}^{\frac {-y \left (x \right ) x +a}{a \left (1+k \right ) x}} y \left (x \right )-\left (\int _{}^{\frac {a x}{-y \left (x \right ) x +a}}\left (\textit {\_a} -1\right )^{\frac {1}{1+k}} {\mathrm e}^{\frac {1}{\left (1+k \right ) \textit {\_a}}} \textit {\_a}^{-\frac {1}{1+k}}d \textit {\_a} -c_{1} \right ) \left (-y \left (x \right ) x +a \right )}{-y \left (x \right ) x +a} = 0 \]

Problem 10793

ODE	\[ \boxed {y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y=a^{2} \left (k -2\right ) \left (x -1\right )^{2} x^{1-2 k}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10794

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2}=\frac {a^{2} \left (-3+2 k \right ) \left (x -1\right )^{2} x^{1-2 k}}{2}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10795

ODE	\[ \boxed {y y^{\prime }-\left (\left (2 n -1\right ) x -n a \right ) x^{-n -1} y=n \left (x -a \right ) x^{-2 n}} \]
program solution
Maple solution	\[ y \left (x \right ) = \frac {2 \left (-\frac {\sqrt {-n^{2}}\, x \tan \left (\frac {\operatorname {RootOf}\left (-2 a n \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}+n x \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-\tan \left (\frac {\textit {\_a} \sqrt {-n^{2}}}{2}\right ) \textit {\_Z} \sqrt {-n^{2}}\, x +2 c_{1} x \,{\mathrm e}^{\textit {\_a}}\right ) \sqrt {-n^{2}}}{2}\right )}{2}+\left (a -\frac {x}{2}\right ) n \right ) x^{-n}}{\tan \left (\frac {\operatorname {RootOf}\left (-2 a n \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}+n x \,{\mathrm e}^{\textit {\_Z} +\textit {\_a}}-\tan \left (\frac {\textit {\_a} \sqrt {-n^{2}}}{2}\right ) \textit {\_Z} \sqrt {-n^{2}}\, x +2 c_{1} x \,{\mathrm e}^{\textit {\_a}}\right ) \sqrt {-n^{2}}}{2}\right ) \sqrt {-n^{2}}+n} \]

Problem 10796

ODE	\[ \boxed {y y^{\prime }-\left (\left (n +1\right ) x -n a \right ) x^{n -1} \left (x -a \right )^{-2-n} y=n \,x^{2 n} \left (x -a \right )^{-2 n -3}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10797

ODE	\[ \boxed {y y^{\prime }-a \left (\left (-3+2 k \right ) x +1\right ) x^{-k} y=a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{-2 k +2}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10798

ODE	\[ \boxed {y y^{\prime }-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y=a^{2} \left (\left (k +n -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10799

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (\left (n +2\right ) x -2\right ) x^{-\frac {1+2 n}{n}} y}{n}=\frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {2+3 n}{n}}}{n}} \]
program solution
Maple solution	\[ \text {No solution found} \]

Problem 10800

ODE	\[ \boxed {y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{n +2}-2\right ) x^{-\frac {1+2 n}{n}} y}{n}=\frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (n +2\right )\right ) x^{-\frac {2+3 n}{n}}}{n \left (n +2\right )}} \]
program solution
Maple solution	\[ \text {No solution found} \]