5.3.59 Problems 5801 to 5900

Table 5.163: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

17349

\[ {} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \]

17350

\[ {} -2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

17351

\[ {} -4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \]

17357

\[ {} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0 \]

17360

\[ {} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \]

17361

\[ {} -1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0 \]

17375

\[ {} \cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \]

17376

\[ {} y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{y+t} = 0 \]

17384

\[ {} t^{2}+t y+y^{2}-t y y^{\prime } = 0 \]

17389

\[ {} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \]

17394

\[ {} t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \]

17397

\[ {} y^{\prime }+2 y = t^{2} \sqrt {y} \]

17398

\[ {} -2 y+y^{\prime } = t^{2} \sqrt {y} \]

17402

\[ {} t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \]

17411

\[ {} y^{\prime }+y \cot \left (x \right ) = y^{4} \]

17412

\[ {} t y^{\prime }-{y^{\prime }}^{3} = y \]

17413

\[ {} t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1 \]

17415

\[ {} 1+y-t y^{\prime } = \ln \left (y^{\prime }\right ) \]

17416

\[ {} 1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}} \]

17417

\[ {} y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \]

17418

\[ {} y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \]

17420

\[ {} y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \]

17421

\[ {} t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0 \]

17439

\[ {} t^{2}-y+\left (y-t \right ) y^{\prime } = 0 \]

17440

\[ {} t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \]

17441

\[ {} \tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0 \]

17449

\[ {} y = t y^{\prime }+3 {y^{\prime }}^{4} \]

17451

\[ {} y-t y^{\prime } = -2 {y^{\prime }}^{3} \]

17455

\[ {} {\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0 \]

17456

\[ {} \sin \left (y\right )-\cos \left (t \right ) y+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0 \]

17458

\[ {} \frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0 \]

17459

\[ {} y^{\prime } = -x +y^{2} \]

17461

\[ {} y^{\prime } = t y^{3} \]

17491

\[ {} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]

17535

\[ {} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0 \]

17536

\[ {} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0 \]

17566

\[ {} y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

17583

\[ {} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t} \]

17624

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \]

17647

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \]

17649

\[ {} t y^{\prime \prime }+2 y^{\prime }+t y = -t \]

17651

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]

17652

\[ {} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \]

17653

\[ {} \left (\sin \left (t \right )-\cos \left (t \right ) t \right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t \]

17691

\[ {} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0 \]

17692

\[ {} 2 y y^{\prime \prime }+y^{2} = {y^{\prime }}^{2} \]

17723

\[ {} t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1 \]

17724

\[ {} \left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime } = -2-t \]

17776

\[ {} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]

17777

\[ {} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = \arctan \left (x \right ) \]

17778

\[ {} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]

17779

\[ {} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = \arctan \left (x \right ) \]

17780

\[ {} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right ) = 0 \]

17781

\[ {} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0 \]

17782

\[ {} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+y \left (x^{2}-1\right ) = 0 \]

17800

\[ {} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{-x} \]

17810

\[ {} y^{\prime \prime }+x y^{\prime } = \sin \left (x \right ) \]

17811

\[ {} y^{\prime \prime }+y^{\prime }+x y = \cos \left (x \right ) \]

17812

\[ {} y^{\prime \prime }+\left (y^{2}-1\right ) y^{\prime }+y = 0 \]

17813

\[ {} y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y = 0 \]

17818

\[ {} y^{\prime \prime }-y \cos \left (x \right ) = \sin \left (x \right ) \]

17819

\[ {} x^{2} y^{\prime \prime }+6 y = 0 \]

17820

\[ {} x \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0 \]

17837

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y = 0 \]

17844

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0 \]

17867

\[ {} y^{\prime \prime }-2 y^{\prime } = \frac {1}{1+{\mathrm e}^{2 t}} \]

17890

\[ {} y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0 \]

17902

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x} \]

17906

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0 \]

17909

\[ {} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime } = 1 \]

17938

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}, y^{\prime }\left (t \right ) = {\mathrm e}^{t}] \]

17951

\[ {} y^{\prime } = x^{2}+y^{2} \]

17955

\[ {} y^{\prime } = \sqrt {-y+x^{2}}-x \]

17958

\[ {} y^{\prime } = \sin \left (y\right )-\cos \left (x \right ) \]

17961

\[ {} y^{\prime } = \sin \left (x y\right ) \]

17971

\[ {} y^{\prime } = x^{2}-y^{2} \]

17985

\[ {} y^{\prime } = x^{2}-y^{2} \]

17986

\[ {} y^{\prime } = x +y^{2} \]

18007

\[ {} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0 \]

18008

\[ {} y^{\prime } = \frac {y}{x} \]

18016

\[ {} x^{2} \cos \left (y\right ) y^{\prime }+1 = 0 \]

18017

\[ {} x^{2} y^{\prime }+\cos \left (2 y\right ) = 1 \]

18018

\[ {} x^{3} y^{\prime }-\sin \left (y\right ) = 1 \]

18019

\[ {} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0 \]

18024

\[ {} x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2} \]

18062

\[ {} 2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}} \]

18071

\[ {} y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}} \]

18079

\[ {} y y^{\prime }+1 = \left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \]

18080

\[ {} y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \]

18082

\[ {} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0 \]

18083

\[ {} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0 \]

18084

\[ {} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0 \]

18085

\[ {} 2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \]

18086

\[ {} \frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0 \]

18087

\[ {} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0 \]

18088

\[ {} \frac {x y}{\sqrt {x^{2}+1}}+2 x y-\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime } = 0 \]

18089

\[ {} \sin \left (y\right )+\sin \left (x \right ) y+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0 \]

18090

\[ {} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0 \]

18091

\[ {} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0 \]

18092

\[ {} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right ) = 0 \]