2.17.150 Problems 14901 to 15000

Problem 14901

ODE	\[ \boxed {10 x^{\prime \prime }+\frac {x}{10}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = -5, x^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ x = -5 \cos \left (\frac {t}{10}\right )+10 \sin \left (\frac {t}{10}\right ) \] Verified OK.
Maple solution	\[ x \left (t \right ) = 10 \sin \left (\frac {t}{10}\right )-5 \cos \left (\frac {t}{10}\right ) \]

Problem 14902

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

Problem 14903

ODE	\[ \boxed {\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = \frac {\left (31+4 \sqrt {62}\right ) {\mathrm e}^{4 \left (-8+\sqrt {62}\right ) t}}{62}+\frac {\left (31-4 \sqrt {62}\right ) {\mathrm e}^{-4 \left (8+\sqrt {62}\right ) t}}{62} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \frac {\left (31+4 \sqrt {62}\right ) {\mathrm e}^{4 \left (-8+\sqrt {62}\right ) t}}{62}+\frac {\left (31-4 \sqrt {62}\right ) {\mathrm e}^{-4 \left (8+\sqrt {62}\right ) t}}{62} \]

Problem 14904

ODE	\[ \boxed {\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x=0} \] With initial conditions \begin {align*} \left [x \left (0\right ) = -{\frac {1}{2}}, x^{\prime }\left (0\right ) = 1\right ] \end {align*}
program solution	\[ x = \frac {\left (-\sqrt {3}-3\right ) {\mathrm e}^{2 \left (-2+\sqrt {3}\right ) t}}{12}+\frac {{\mathrm e}^{-2 \left (2+\sqrt {3}\right ) t} \left (\sqrt {3}-3\right )}{12} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \frac {\left (-3-\sqrt {3}\right ) {\mathrm e}^{2 \left (-2+\sqrt {3}\right ) t}}{12}+\frac {{\mathrm e}^{-2 \left (2+\sqrt {3}\right ) t} \left (\sqrt {3}-3\right )}{12} \]

Problem 14905

ODE	\[ \boxed {4 x^{\prime \prime }+2 x^{\prime }+8 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 2] \end {align*}
program solution	\[ x = \frac {8 \sqrt {31}\, {\mathrm e}^{-\frac {t}{4}} \sin \left (\frac {\sqrt {31}\, t}{4}\right )}{31} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \frac {8 \sqrt {31}\, {\mathrm e}^{-\frac {t}{4}} \sin \left (\frac {\sqrt {31}\, t}{4}\right )}{31} \]

Problem 14906

ODE	\[ \boxed {x^{\prime \prime }+4 x^{\prime }+13 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = -1] \end {align*}
program solution	\[ x = \frac {{\mathrm e}^{-2 t} \left (3 \cos \left (3 t \right )+\sin \left (3 t \right )\right )}{3} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \frac {{\mathrm e}^{-2 t} \left (\sin \left (3 t \right )+3 \cos \left (3 t \right )\right )}{3} \]

Problem 14907

ODE	\[ \boxed {x^{\prime \prime }+4 x^{\prime }+20 x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1, x^{\prime }\left (0\right ) = 2] \end {align*}
program solution	\[ x = {\mathrm e}^{-2 t} \left (\cos \left (4 t \right )+\sin \left (4 t \right )\right ) \] Verified OK.
Maple solution	\[ x \left (t \right ) = {\mathrm e}^{-2 t} \left (\sin \left (4 t \right )+\cos \left (4 t \right )\right ) \]

Problem 14908

ODE	\[ \boxed {x^{\prime \prime }+x=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = \left \{\begin {array}{cc} 0 & t \le 0 \\ 1-\cos \left (t \right ) & t \le \pi \\ -2 \cos \left (t \right ) & \pi
Maple solution	\[ x \left (t \right ) = \left \{\begin {array}{cc} 0 & t <0 \\ -\cos \left (t \right )+1 & t <\pi \\ -2 \cos \left (t \right ) & \pi \le t \end {array}\right . \]

Problem 14909

ODE	\[ \boxed {x^{\prime \prime }+x=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = \frac {\sin \left (t \right ) \left (\left \{\begin {array}{cc} 0 & t \le 0 \\ t & t \le \pi \\ \pi & \pi
Maple solution	\[ x \left (t \right ) = \frac {\sin \left (t \right ) \left (\left \{\begin {array}{cc} 0 & t <0 \\ t & t <\pi \\ \pi & \pi \le t \end {array}\right .\right )}{2} \]

Problem 14910

ODE	\[ \boxed {x^{\prime \prime }+x=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = \left \{\begin {array}{cc} 0 & t \le 0 \\ -\sin \left (t \right )+t & t \le 1 \\ \left (-1+2 \cos \left (1\right )\right ) \sin \left (t \right )-2 \cos \left (t \right ) \sin \left (1\right )-t +2 & t \le 2 \\ -2 \left (\sin \left (t \right ) \cos \left (1\right )-\cos \left (t \right ) \sin \left (1\right )\right ) \left (-1+\cos \left (1\right )\right ) & 2
Maple solution	\[ x \left (t \right ) = \left \{\begin {array}{cc} 0 & t <0 \\ t -\sin \left (t \right ) & t <1 \\ 2 \sin \left (t -1\right )-\sin \left (t \right )-t +2 & t <2 \\ 2 \sin \left (t -1\right )-\sin \left (t \right )-\sin \left (t -2\right ) & 2\le t \end {array}\right . \]

Problem 14911

ODE	\[ \boxed {x^{\prime \prime }+4 x^{\prime }+13 x=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = -\frac {\left (\left \{\begin {array}{cc} 0 & t \le 0 \\ -3+{\mathrm e}^{-2 t} \left (2 \sin \left (3 t \right )+3 \cos \left (3 t \right )\right ) & t \le \pi \\ \frac {\left (\left (39 \pi -12\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (26 \pi +5\right )\right ) {\mathrm e}^{-2 t +2 \pi }}{13}+3 \,{\mathrm e}^{-2 t} \cos \left (3 t \right )+2 \,{\mathrm e}^{-2 t} \sin \left (3 t \right )+3 t -\frac {51}{13} & t \le 2 \pi \\ \frac {\left (\left (39 \pi -12\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (26 \pi +5\right )\right ) {\mathrm e}^{-2 t +2 \pi }}{13}+\frac {\left (\left (78 \pi -51\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (52 \pi -21\right )\right ) {\mathrm e}^{-2 t +4 \pi }}{13}+3 \left (\cos \left (3 t \right )+\frac {2 \sin \left (3 t \right )}{3}\right ) {\mathrm e}^{-2 t} & 2 \pi
Maple solution	\[ x \left (t \right ) = -\frac {\left (\left \{\begin {array}{cc} 0 & t <0 \\ -3+\left (3 \cos \left (3 t \right )+2 \sin \left (3 t \right )\right ) {\mathrm e}^{-2 t} & t <\pi \\ \frac {\left (\left (39 \pi -12\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (26 \pi +5\right )\right ) {\mathrm e}^{-2 t +2 \pi }}{13}+3 \,{\mathrm e}^{-2 t} \cos \left (3 t \right )+2 \,{\mathrm e}^{-2 t} \sin \left (3 t \right )+3 t -\frac {51}{13} & t <2 \pi \\ \frac {\left (\left (78 \pi -51\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (52 \pi -21\right )\right ) {\mathrm e}^{4 \pi -2 t}}{13}+\frac {\left (\left (39 \pi -12\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (26 \pi +5\right )\right ) {\mathrm e}^{-2 t +2 \pi }}{13}+3 \,{\mathrm e}^{-2 t} \left (\cos \left (3 t \right )+\frac {2 \sin \left (3 t \right )}{3}\right ) & 2 \pi \le t \end {array}\right .\right )}{39} \]

Problem 14912

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

Problem 14913

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

Problem 14914

ODE	\[ \boxed {x^{\prime \prime }+x=\cos \left (\frac {9 t}{10}\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ x = -\frac {100 \cos \left (t \right )}{19}+\sin \left (t \right )+\frac {100 \cos \left (\frac {9 t}{10}\right )}{19} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \sin \left (t \right )-\frac {100 \cos \left (t \right )}{19}+\frac {100 \cos \left (\frac {9 t}{10}\right )}{19} \]

Problem 14915

ODE	\[ \boxed {x^{\prime \prime }+x=\cos \left (\frac {7 t}{10}\right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 1] \end {align*}
program solution	\[ x = -\frac {100 \cos \left (t \right )}{51}+\sin \left (t \right )+\frac {100 \cos \left (\frac {7 t}{10}\right )}{51} \] Verified OK.
Maple solution	\[ x \left (t \right ) = \sin \left (t \right )-\frac {100 \cos \left (t \right )}{51}+\frac {100 \cos \left (\frac {7 t}{10}\right )}{51} \]

Problem 14916

ODE	\[ \boxed {x^{\prime \prime }+\frac {x^{\prime }}{10}+x=3 \cos \left (2 t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
program solution	\[ x = \frac {225 \,{\mathrm e}^{-\frac {t}{20}} \cos \left (\frac {\sqrt {399}\, t}{20}\right )}{226}-\frac {125 \,{\mathrm e}^{-\frac {t}{20}} \sin \left (\frac {\sqrt {399}\, t}{20}\right ) \sqrt {399}}{30058}-\frac {225 \cos \left (2 t \right )}{226}+\frac {15 \sin \left (2 t \right )}{226} \] Verified OK.
Maple solution	\[ x \left (t \right ) = -\frac {125 \,{\mathrm e}^{-\frac {t}{20}} \sqrt {399}\, \sin \left (\frac {\sqrt {399}\, t}{20}\right )}{30058}+\frac {225 \,{\mathrm e}^{-\frac {t}{20}} \cos \left (\frac {\sqrt {399}\, t}{20}\right )}{226}-\frac {225 \cos \left (2 t \right )}{226}+\frac {15 \sin \left (2 t \right )}{226} \]

Problem 14917

ODE	\begin {align*} x^{\prime }&=6\\ y^{\prime }\left (t \right )&=\cos \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= 6 t +c_{2} \\ y \left (t \right ) &= \sin \left (t \right )+c_{1} \\ \end{align*}

Problem 14918

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

Problem 14919

ODE	\begin {align*} x^{\prime }&=0\\ y^{\prime }\left (t \right )&=-2 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= c_{2} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{-2 t} \\ \end{align*}

Problem 14920

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

Problem 14921

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

Problem 14922

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

Problem 14923

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

Problem 14924

ODE	\begin {align*} x^{\prime }&=8 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=x+6 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= {\mathrm e}^{7 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}

Problem 14925

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

Problem 14926

ODE	\begin {align*} x^{\prime }&=4 x+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x+2 y \left (t \right ) \end {align*}
program solution
Maple solution	\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 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 14927

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

Problem 14928

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

Problem 14929

ODE	\[ \boxed {x^{\prime \prime }-3 x^{\prime }+4 x=0} \]
program solution	\[ x = c_{1} {\mathrm e}^{\frac {3 t}{2}} \cos \left (\frac {\sqrt {7}\, t}{2}\right )+\frac {2 c_{2} \sin \left (\frac {\sqrt {7}\, t}{2}\right ) {\mathrm e}^{\frac {3 t}{2}} \sqrt {7}}{7} \] Verified OK.
Maple solution	\[ x \left (t \right ) = {\mathrm e}^{\frac {3 t}{2}} \left (c_{1} \sin \left (\frac {\sqrt {7}\, t}{2}\right )+c_{2} \cos \left (\frac {\sqrt {7}\, t}{2}\right )\right ) \]

Problem 14930

ODE	\[ \boxed {x^{\prime \prime }+6 x^{\prime }+9 x=0} \]
program solution	\[ x = c_{1} {\mathrm e}^{-3 t}+c_{2} t \,{\mathrm e}^{-3 t} \] Verified OK.
Maple solution	\[ x \left (t \right ) = {\mathrm e}^{-3 t} \left (t c_{2} +c_{1} \right ) \]

Problem 14931

ODE	\[ \boxed {x^{\prime \prime }+16 x=t \sin \left (t \right )} \]
program solution	\[ x = c_{1} \cos \left (4 t \right )+\frac {c_{2} \sin \left (4 t \right )}{4}+\frac {t \sin \left (t \right )}{15}-\frac {2 \cos \left (t \right )}{225} \] Verified OK.
Maple solution	\[ x \left (t \right ) = c_{2} \sin \left (4 t \right )+c_{1} \cos \left (4 t \right )-\frac {2 \cos \left (t \right )}{225}+\frac {\sin \left (t \right ) t}{15} \]

Problem 14932

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

Problem 14933

ODE	\[ \boxed {y^{\prime }-y^{2}=x^{2}} \]
program solution	\[ y = -\frac {x \left (\operatorname {BesselY}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right )+\operatorname {BesselJ}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) c_{3} \right )}{\operatorname {BesselJ}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_{3} +\operatorname {BesselY}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {x \left (\operatorname {BesselJ}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right ) c_{1} +\operatorname {BesselY}\left (-\frac {3}{4}, \frac {x^{2}}{2}\right )\right )}{c_{1} \operatorname {BesselJ}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )+\operatorname {BesselY}\left (\frac {1}{4}, \frac {x^{2}}{2}\right )} \]

Problem 14934

ODE	\[ \boxed {y^{\prime }-\frac {x}{y}=0} \]
program solution	\[ \frac {y^{2}}{2}-\frac {x^{2}}{2} = c_{1} \] 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 14935

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

Problem 14936

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

Problem 14937

ODE	\[ \boxed {y^{\prime }-\sqrt {x^{2}-y}=-x} \]
program solution	\[ \frac {3 \ln \left (5 x^{2}+4 y\right )}{10}+\frac {\ln \left (y\right )}{5}+\frac {3 \ln \left (2 \sqrt {x^{2}-y}+3 x \right )}{10}+\frac {\ln \left (\sqrt {x^{2}-y}-x \right )}{5}-\frac {3 \ln \left (-3 x +2 \sqrt {x^{2}-y}\right )}{10}-\frac {\ln \left (x +\sqrt {x^{2}-y}\right )}{5} = c_{1} \] Verified OK.
Maple solution	\[ \frac {250 \left (x^{6} c_{1} y \left (x \right )^{2}+\frac {12 x^{4} c_{1} y \left (x \right )^{3}}{5}+\frac {48 x^{2} c_{1} y \left (x \right )^{4}}{25}+\frac {64 c_{1} y \left (x \right )^{5}}{125}-\frac {1}{125}\right ) \left (x^{2}-y \left (x \right )\right )^{\frac {3}{2}} \left (x^{2}+4 y \left (x \right )\right )-250 \left (x^{6} c_{1} y \left (x \right )^{2}+\frac {12 x^{4} c_{1} y \left (x \right )^{3}}{5}+\frac {48 x^{2} c_{1} y \left (x \right )^{4}}{25}+\frac {64 c_{1} y \left (x \right )^{5}}{125}+\frac {1}{125}\right ) \left (x^{4}+\frac {5 y \left (x \right ) x^{2}}{2}+10 y \left (x \right )^{2}\right ) x}{\left (5 x^{2}+4 y \left (x \right )\right )^{3} y \left (x \right )^{2} \left (-\sqrt {x^{2}-y \left (x \right )}+x \right )^{2} \left (3 x +2 \sqrt {x^{2}-y \left (x \right )}\right )^{3}} = 0 \]

Problem 14938

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

Problem 14939

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

Problem 14940

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

Problem 14941

ODE	\[ \boxed {y^{\prime }+\cot \left (y\right )=1} \]
program solution	\[ \frac {y}{2}+\frac {\ln \left (\tan \left (y\right )-1\right )}{2}-\frac {\ln \left (\sec \left (y\right )^{2}\right )}{4} = x +c_{1} \] Verified OK.
Maple solution	\[ x +\frac {\ln \left (\csc \left (y \left (x \right )\right )^{2}\right )}{4}+\frac {\pi }{4}-\frac {\ln \left (-1+\cot \left (y \left (x \right )\right )\right )}{2}-\frac {y \left (x \right )}{2}+c_{1} = 0 \]

Problem 14942

ODE	\[ \boxed {y^{\prime }-\left (-y+3 x \right )^{\frac {1}{3}}=-1} \]
program solution	\[ \frac {3 \left (-y+3 x \right )^{\frac {2}{3}}}{2}-16 \ln \left (\left (-y+3 x \right )^{\frac {2}{3}}+4 \left (-y+3 x \right )^{\frac {1}{3}}+16\right )+32 \ln \left (-4+\left (-y+3 x \right )^{\frac {1}{3}}\right )+16 \ln \left (-64-y+3 x \right )+12 \left (-y+3 x \right )^{\frac {1}{3}} = -x +c_{1} \] Verified OK.
Maple solution	\[ x +\frac {3 \left (3 x -y \left (x \right )\right )^{\frac {2}{3}}}{2}+32 \ln \left (-4+\left (3 x -y \left (x \right )\right )^{\frac {1}{3}}\right )-16 \ln \left (\left (3 x -y \left (x \right )\right )^{\frac {2}{3}}+4 \left (3 x -y \left (x \right )\right )^{\frac {1}{3}}+16\right )+16 \ln \left (-64+3 x -y \left (x \right )\right )+12 \left (3 x -y \left (x \right )\right )^{\frac {1}{3}}-c_{1} = 0 \]

Problem 14943

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

Problem 14944

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

Problem 14945

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

Problem 14946

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

Problem 14947

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

Problem 14948

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

Problem 14949

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

Problem 14950

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

Problem 14951

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

Problem 14952

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

Problem 14953

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

Problem 14954

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

Problem 14955

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

Problem 14956

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

Problem 14957

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

Problem 14958

ODE	\[ \boxed {y^{\prime }-\frac {x +y}{x -y}=0} \]
program solution	\[ \frac {\ln \left (y^{2}+x^{2}\right )}{2}+\arctan \left (\frac {x}{y}\right ) = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

Problem 14959

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

Problem 14960

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

Problem 14961

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

Problem 14962

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

Problem 14963

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

Problem 14964

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

Problem 14965

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

Problem 14966

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

Problem 14967

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

Problem 14968

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

Problem 14969

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

Problem 14970

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

Problem 14971

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

Problem 14972

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 14973

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

Problem 14974

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

Problem 14975

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

Problem 14976

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

Problem 14977

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

Problem 14978

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

Problem 14979

ODE	\[ \boxed {\ln \left (y\right ) y+y^{\prime } x=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
program solution	\[ -\ln \left (x \right )-\left (\int _{0}^{y}\frac {1}{\ln \left (\textit {\_a} \right ) \textit {\_a} -1}d \textit {\_a} \right ) = -\left (\int _{0}^{1}\frac {1}{\ln \left (\textit {\_a} \right ) \textit {\_a} -1}d \textit {\_a} \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{1}^{\textit {\_Z}}\frac {1}{\ln \left (\textit {\_a} \right ) \textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )\right ) \]

Problem 14980

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

Problem 14981

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

Problem 14982

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

Problem 14983

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

Problem 14984

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

Problem 14985

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

Problem 14986

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

Problem 14987

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

Problem 14988

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

Problem 14989

ODE	\[ \boxed {y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }=-a^{2}} \] With initial conditions \begin {align*} [y \left (a \right ) = 0] \end {align*}
program solution	N/A
Maple solution	\[ y \left (x \right ) = \tan \left (\frac {a -x}{\sqrt {x \left (a -x \right )}}\right ) a \]

Problem 14990

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

Problem 14991

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

Problem 14992

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

Problem 14993

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

Problem 14994

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

Problem 14995

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

Problem 14996

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

Problem 14997

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

Problem 14998

ODE	\[ \boxed {x^{2} y^{\prime } \cos \left (y\right )=-1} \] With initial conditions \begin {align*} \left [y \left (\infty \right ) = \frac {16 \pi }{3}\right ] \end {align*}
program solution	\[ \frac {1}{x}-\sin \left (y\right ) = \frac {\sqrt {3}}{2} \] Warning, solution could not be verified
Maple solution	\[ y = \arcsin \left (\frac {\sqrt {3}\, x -2}{2 x}\right )+5 \pi \]

Problem 14999

ODE	\[ \boxed {x^{2} y^{\prime }+\cos \left (2 y\right )=1} \] With initial conditions \begin {align*} \left [y \left (\infty \right ) = \frac {10 \pi }{3}\right ] \end {align*}
program solution	\[ \frac {1}{x}-\frac {\cot \left (y\right )}{2} = -\frac {\sqrt {3}}{6} \] Warning, solution could not be verified
Maple solution	\[ y = \frac {7 \pi }{2}-\arctan \left (\frac {\sqrt {3}\, x +6}{3 x}\right ) \]

Problem 15000

ODE	\[ \boxed {y^{\prime } x^{3}-\sin \left (y\right )=1} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 5 \pi ] \end {align*}
program solution	\[ \frac {1}{2 x^{2}}-\frac {2}{\tan \left (\frac {y}{2}\right )+1} = 0 \] Verified OK.
Maple solution	\[ \text {No solution found} \]