2.17.134 Problems 13301 to 13400

Problem 13301

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

Problem 13302

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

Problem 13303

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

Problem 13304

ODE	\[ \boxed {y^{\prime }+4 y=x^{2}} \]
program solution	\[ y = \frac {\left (8 x^{2} {\mathrm e}^{4 x}-4 x \,{\mathrm e}^{4 x}+{\mathrm e}^{4 x}+32 c_{1} \right ) {\mathrm e}^{-4 x}}{32} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {x^{2}}{4}-\frac {x}{8}+\frac {1}{32}+{\mathrm e}^{-4 x} c_{1} \]

Problem 13305

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

Problem 13306

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	\[ y \left (x \right ) = -x -2 \arctan \left (\frac {c_{1} -x -2}{c_{1} -x}\right ) \]

Problem 13307

ODE	\[ \boxed {y y^{\prime }-{\mathrm e}^{x -3 y^{2}}=0} \]
program solution	\[ \frac {{\mathrm e}^{3 y^{2}}}{6}-{\mathrm e}^{x} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_{1} \right )}}{3} \\ y \left (x \right ) &= \frac {\sqrt {3}\, \sqrt {\ln \left (2\right )+\ln \left (3\right )+\ln \left ({\mathrm e}^{x}+c_{1} \right )}}{3} \\ \end{align*}

Problem 13308

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 13309

ODE	\[ \boxed {y^{\prime }-y^{2}=9} \]
program solution	\[ y = 3 \tan \left (3 c_{1} +3 x \right ) \] Verified OK.
Maple solution	\[ y \left (x \right ) = 3 \tan \left (3 c_{1} +3 x \right ) \]

Problem 13310

ODE	\[ \boxed {x y y^{\prime }-y^{2}=9} \]
program solution	\[ -\ln \left (x \right )+\frac {\ln \left (y^{2}+9\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x^{2}-9} \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}-9} \\ \end{align*}

Problem 13311

ODE	\[ \boxed {y^{\prime }-\frac {1+y^{2}}{x^{2}+1}=0} \]
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 13312

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

Problem 13313

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

Problem 13314

ODE	\[ \boxed {y^{\prime }-\frac {x}{y}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
program solution	\[ \frac {y^{2}}{2}-\frac {x^{2}}{2} = 4 \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x^{2}+8} \]

Problem 13315

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

Problem 13316

ODE	\[ \boxed {y y^{\prime }-x y^{2}=x} \] With initial conditions \begin {align*} [y \left (0\right ) = -2] \end {align*}
program solution	\[ -\frac {x^{2}}{2}+\frac {\ln \left (1+y^{2}\right )}{2} = \frac {\ln \left (5\right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\sqrt {5 \,{\mathrm e}^{x^{2}}-1} \]

Problem 13317

ODE	\[ \boxed {y y^{\prime }-3 \sqrt {x y^{2}+9 x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 4] \end {align*}
program solution	\[ \frac {-2 x \sqrt {x \left (y^{2}+9\right )}+y^{2}+9}{\sqrt {y^{2}+9}} = 3 \] Verified OK.
Maple solution	\[ y \left (x \right ) = 2 \sqrt {x^{\frac {3}{2}} \left (x^{\frac {3}{2}}+3\right )} \]

Problem 13318

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

Problem 13319

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

Problem 13320

ODE	\[ \boxed {y y^{\prime }-x y^{2}=-9 x} \]
program solution	\[ -\frac {x^{2}}{2}+\frac {\ln \left (y^{2}-9\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} +9} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} +9} \\ \end{align*}

Problem 13321

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

Problem 13322

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

Problem 13323

ODE	\[ \boxed {y^{\prime }-200 y+2 y^{2}=0} \]
program solution	\[ y = \frac {100 \,{\mathrm e}^{200 x} c_{1}^{200}}{-1+{\mathrm e}^{200 x} c_{1}^{200}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {100}{1+100 \,{\mathrm e}^{-200 x} c_{1}} \]

Problem 13324

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

Problem 13325

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

Problem 13326

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

Problem 13327

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

Problem 13328

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

Problem 13329

ODE	\[ \boxed {y^{\prime }-\frac {6 x^{2}+4}{3 y^{2}-4 y}=0} \]
program solution	\[ -x^{3}-2 x +\frac {y^{3}}{2}-y^{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {\left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {2}{3}}+2 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}+4}{3 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {2}{3}}-4 i \sqrt {3}-4 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}+4}{6 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {2}{3}}-4 i \sqrt {3}+4 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}-4}{6 \left (8+27 x^{3}+27 c_{1} +54 x +3 \sqrt {81}\, \sqrt {\left (x^{3}+c_{1} +2 x +\frac {16}{27}\right ) \left (x^{3}+c_{1} +2 x \right )}\right )^{\frac {1}{3}}} \\ \end{align*}

Problem 13330

ODE	\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-y^{2}=1} \]
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 13331

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

Problem 13332

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

Problem 13333

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

Problem 13334

ODE	\[ \boxed {y^{\prime }-3 x y^{3}=0} \]
program solution	\[ -\frac {x^{2}}{2}-\frac {1}{6 y^{2}} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {-3 x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {-3 x^{2}+c_{1}}} \\ \end{align*}

Problem 13335

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

Problem 13336

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

Problem 13337

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

Problem 13338

ODE	\[ \boxed {y^{\prime }-200 y+2 y^{2}=0} \]
program solution	\[ y = \frac {100 \,{\mathrm e}^{200 x} c_{1}^{200}}{-1+{\mathrm e}^{200 x} c_{1}^{200}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {100}{1+100 \,{\mathrm e}^{-200 x} c_{1}} \]

Problem 13339

ODE	\[ \boxed {y^{\prime }-2 y=-10} \] With initial conditions \begin {align*} [y \left (0\right ) = 8] \end {align*}
program solution	\[ \frac {\ln \left (y-5\right )}{2} = x +\frac {\ln \left (3\right )}{2} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 5+3 \,{\mathrm e}^{2 x} \]

Problem 13340

ODE	\[ \boxed {y y^{\prime }=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -4] \end {align*}
program solution	\[ \frac {y^{2}}{2}+\cos \left (x \right ) = 9 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\sqrt {18-2 \cos \left (x \right )} \]

Problem 13341

ODE	\[ \boxed {y^{\prime }-2 y x +y=2 x -1} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
program solution	N/A
Maple solution	\[ y \left (x \right ) = -1 \]

Problem 13342

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

Problem 13343

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

Problem 13344

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

Problem 13345

ODE	\[ \boxed {\left (-1+y^{2}\right ) y^{\prime }-4 y x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
program solution	N/A
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-2 x^{2}-\frac {1}{2}}}{\sqrt {-\frac {{\mathrm e}^{-4 x^{2}-1}}{\operatorname {LambertW}\left (-{\mathrm e}^{-4 x^{2}-1}\right )}}} \]

Problem 13346

ODE	\[ \boxed {x^{2} y^{\prime }+3 y x^{2}=\sin \left (x \right )} \]
program solution	\[ \int _{}^{x}\frac {\left (3 \textit {\_a}^{2} y-\sin \left (\textit {\_a} \right )\right ) {\mathrm e}^{3 \textit {\_a}}}{\textit {\_a}^{2}}d \textit {\_a} = c_{1} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {3 \left (\left (-\frac {1}{3}+i\right ) x \,\operatorname {expIntegral}_{1}\left (\left (-3-i\right ) x \right )+\left (-\frac {1}{3}-i\right ) x \,\operatorname {expIntegral}_{1}\left (\left (-3+i\right ) x \right )-\frac {i {\mathrm e}^{\left (3-i\right ) x}}{3}+\frac {i {\mathrm e}^{\left (3+i\right ) x}}{3}+\frac {2 c_{1} x}{3}\right ) {\mathrm e}^{-3 x}}{2 x} \]

Problem 13347

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

Problem 13348

ODE	\[ \boxed {y^{\prime }-x y^{2}=\sqrt {x}} \]
program solution	\[ y = -\frac {\operatorname {BesselJ}\left (-\frac {3}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right ) c_{3} +\operatorname {BesselY}\left (-\frac {3}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right )}{x^{\frac {1}{4}} \left (c_{3} \operatorname {BesselJ}\left (\frac {4}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right )+\operatorname {BesselY}\left (\frac {4}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right )\right )} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\operatorname {BesselY}\left (-\frac {3}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right ) c_{1} +\operatorname {BesselJ}\left (-\frac {3}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right )}{x^{\frac {1}{4}} \left (\operatorname {BesselY}\left (\frac {4}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right ) c_{1} +\operatorname {BesselJ}\left (\frac {4}{7}, \frac {4 x^{\frac {7}{4}}}{7}\right )\right )} \]

Problem 13349

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

Problem 13350

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

Problem 13351

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

Problem 13352

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

Problem 13353

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

Problem 13354

ODE	\[ \boxed {y^{\prime }+4 y-y^{3}=0} \]
program solution	\[ y = -\frac {2}{\sqrt {1-{\mathrm e}^{8 x} c_{1}^{8}}} \] Verified OK. \[ y = \frac {2}{\sqrt {1-{\mathrm e}^{8 x} c_{1}^{8}}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ y \left (x \right ) &= \frac {2}{\sqrt {4 \,{\mathrm e}^{8 x} c_{1} +1}} \\ \end{align*}

Problem 13355

ODE	\[ \boxed {y^{\prime } x -827 y=-\cos \left (x^{2}\right )} \]
program solution	\[ \text {Expression too large to display} \] Warning, solution could not be verified
Maple solution	\[ y \left (x \right ) = \left (-\left (\int \frac {\cos \left (x^{2}\right )}{x^{828}}d x \right )+c_{1} \right ) x^{827} \]

Problem 13356

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

Problem 13357

ODE	\[ \boxed {y^{\prime }+2 y=20 \,{\mathrm e}^{3 x}} \]
program solution	\[ y = \left (4 \,{\mathrm e}^{5 x}+c_{1} \right ) {\mathrm e}^{-2 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \left (4 \,{\mathrm e}^{5 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]

Problem 13358

ODE	\[ \boxed {y^{\prime }-4 y=16 x} \]
program solution	\[ y = -\left (4 x \,{\mathrm e}^{-4 x}+{\mathrm e}^{-4 x}-c_{1} \right ) {\mathrm e}^{4 x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -4 x -1+c_{1} {\mathrm e}^{4 x} \]

Problem 13359

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

Problem 13360

ODE	\[ \boxed {y^{\prime } x +3 y=10 x^{2}} \]
program solution	\[ y = \frac {2 x^{5}+c_{1}}{x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {2 x^{5}+c_{1}}{x^{3}} \]

Problem 13361

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

Problem 13362

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

Problem 13363

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

Problem 13364

ODE	\[ \boxed {y^{\prime } x +\left (5 x +2\right ) y=\frac {20}{x}} \]
program solution	\[ y = \frac {\left (4 \,{\mathrm e}^{5 x}+c_{1} \right ) {\mathrm e}^{-5 x}}{x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {{\mathrm e}^{-5 x} c_{1} +4}{x^{2}} \]

Problem 13365

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

Problem 13366

ODE	\[ \boxed {-3 y+y^{\prime }=6} \] With initial conditions \begin {align*} [y \left (0\right ) = 5] \end {align*}
program solution	\[ \frac {\ln \left (y+2\right )}{3} = x +\frac {\ln \left (7\right )}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2+7 \,{\mathrm e}^{3 x} \]

Problem 13367

ODE	\[ \boxed {-3 y+y^{\prime }=6} \] With initial conditions \begin {align*} [y \left (0\right ) = -2] \end {align*}
program solution	\[ y = -2 \] Verified OK.
Maple solution	\[ y \left (x \right ) = -2 \]

Problem 13368

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

Problem 13369

ODE	\[ \boxed {y^{\prime } x +3 y=20 x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 10] \end {align*}
program solution	\[ y = \frac {4 x^{5}+6}{x^{3}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {4 x^{5}+6}{x^{3}} \]

Problem 13370

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

Problem 13371

ODE	\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-x \left (3+3 x^{2}-y\right )=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 8] \end {align*}
program solution	\[ y = \frac {x^{2} \sqrt {x^{2}+1}+\sqrt {x^{2}+1}+3 \sqrt {5}}{\sqrt {x^{2}+1}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = x^{2}+1+\frac {3 \sqrt {5}}{\sqrt {x^{2}+1}} \]

Problem 13372

ODE	\[ \boxed {y^{\prime }+6 y x=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
program solution	\[ y = {\mathrm e}^{-3 x^{2}} \left (\int _{0}^{x}{\mathrm e}^{3 \textit {\_a}^{2}} \sin \left (\textit {\_a} \right )d \textit {\_a} \right )+4 \,{\mathrm e}^{-3 x^{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = 4 \,{\mathrm e}^{-3 x^{2}}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}}{6}\right )}{6}+\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x +1\right )}{6}\right )}{12}-\frac {\sqrt {3}\, \sqrt {\pi }\, {\mathrm e}^{-3 x^{2}+\frac {1}{12}} \operatorname {erf}\left (\frac {\sqrt {3}\, \left (6 i x -1\right )}{6}\right )}{12} \]

Problem 13373

ODE	\[ \boxed {x^{2} y^{\prime }+y x=\sqrt {x}\, \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (2\right ) = 5] \end {align*}
program solution	\[ y = \frac {\sqrt {2}\, \sqrt {\pi }\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, \sqrt {x}}{\sqrt {\pi }}\right )-\sqrt {2}\, \sqrt {\pi }\, \operatorname {FresnelS}\left (\frac {2}{\sqrt {\pi }}\right )+10}{x} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, \sqrt {x}}{\sqrt {\pi }}\right )+10-\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {2}{\sqrt {\pi }}\right )}{x} \]

Problem 13374

ODE	\[ \boxed {y^{\prime } x -y=x^{2} {\mathrm e}^{-x^{2}}} \] With initial conditions \begin {align*} [y \left (3\right ) = 8] \end {align*}
program solution	\[ y = \frac {\sqrt {\pi }\, \operatorname {erf}\left (x \right ) x}{2}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (3\right ) x}{2}+\frac {8 x}{3} \] Verified OK.
Maple solution	\[ y \left (x \right ) = -\frac {\left (-\frac {16}{3}+\left (\operatorname {erf}\left (3\right )-\operatorname {erf}\left (x \right )\right ) \sqrt {\pi }\right ) x}{2} \]

Problem 13375

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

Problem 13376

ODE	\[ \boxed {y^{\prime }-\frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}={\frac {3}{2}}} \]
program solution	\[ \frac {{\mathrm e}^{4 x} \left (9 x^{2}-12 y x +4 y^{2}+1\right )}{2} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {3 x}{2}-\frac {\sqrt {{\mathrm e}^{-4 x} c_{1} -1}}{2} \\ y \left (x \right ) &= \frac {3 x}{2}+\frac {\sqrt {{\mathrm e}^{-4 x} c_{1} -1}}{2} \\ \end{align*}

Problem 13377

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

Problem 13378

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

Problem 13379

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

Problem 13380

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

Problem 13381

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

Problem 13382

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

Problem 13383

ODE	\[ \boxed {y^{\prime }+3 y-3 y^{3}=0} \]
program solution	\[ y = \frac {1}{\sqrt {1-{\mathrm e}^{6 x} c_{1}^{6}}} \] Verified OK. \[ y = -\frac {1}{\sqrt {1-{\mathrm e}^{6 x} c_{1}^{6}}} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{6 x} c_{1} +1}} \\ \end{align*}

Problem 13384

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

Problem 13385

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

Problem 13386

ODE	\[ \boxed {y^{\prime }-\frac {y}{x}-\frac {1}{y}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
program solution	\[ \frac {y^{2}+2 x}{2 x^{2}} = {\frac {11}{2}} \] Verified OK.
Maple solution	\[ y \left (x \right ) = \sqrt {x \left (11 x -2\right )} \]

Problem 13387

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

Problem 13388

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

Problem 13389

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

Problem 13390

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

Problem 13391

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

Problem 13392

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

Problem 13393

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

Problem 13394

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

Problem 13395

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

Problem 13396

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

Problem 13397

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

Problem 13398

ODE	\[ \boxed {y^{\prime }+3 y-\frac {28 \,{\mathrm e}^{2 x}}{y^{3}}=0} \]
program solution	\[ \frac {y^{4} {\mathrm e}^{12 x}}{4}-2 \,{\mathrm e}^{14 x} = c_{1} \] Verified OK.
Maple solution	\begin{align*} y \left (x \right ) &= \left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} \\ y \left (x \right ) &= -\left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} \\ y \left (x \right ) &= -i \left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} \\ y \left (x \right ) &= i \left (8 \,{\mathrm e}^{14 x}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-3 x} \\ \end{align*}

Problem 13399

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

Problem 13400

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