6.187 Problems 18601 to 18700

Table 6.373: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18601

\[ {} x +y y^{\prime } {\mathrm e}^{-x} = 0 \]

18602

\[ {} r^{\prime } = \frac {r^{2}}{\theta } \]

18603

\[ {} y^{\prime } = \frac {3 x}{y+x^{2} y} \]

18604

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

18605

\[ {} y^{\prime } = 2 x y^{2}+4 y^{2} x^{3} \]

18606

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

18607

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

18608

\[ {} y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6} \]

18609

\[ {} y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \]

18610

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

18611

\[ {} y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \]

18612

\[ {} 2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}} \]

18613

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

18614

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

18615

\[ {} y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y} \]

18616

\[ {} y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6} \]

18617

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

18618

\[ {} y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y} \]

18619

\[ {} y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y} \]

18620

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

18621

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

18622

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

18623

\[ {} y^{\prime } = \frac {a y+b}{d +c y} \]

18624

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

18625

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

18626

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

18627

\[ {} \frac {y}{t}+y^{\prime } = 5+\cos \left (2 t \right ) \]

18628

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

18629

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

18630

\[ {} 2 t y+y^{\prime } = 16 t \,{\mathrm e}^{-t^{2}} \]

18631

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

18632

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

18633

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

18634

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

18635

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

18636

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

18637

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

18638

\[ {} t y^{\prime }+4 y = t^{2}-t +1 \]

18639

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

18640

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

18641

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

18642

\[ {} 4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t} \]

18643

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

18644

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

18645

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

18646

\[ {} -2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \]

18647

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

18648

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

18649

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

18650

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

18651

\[ {} y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4} \]

18652

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

18653

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

18654

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

18655

\[ {} y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t} \]

18656

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

18657

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

18658

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

18659

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

18660

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

18661

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

18662

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

18663

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

18664

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

18665

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

18666

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

18667

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

18668

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

18669

\[ {} y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \]

18670

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

18671

\[ {} y^{\prime } = y^{{1}/{3}} \]

18672

\[ {} y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \]

18673

\[ {} y^{\prime } = -\frac {4 t}{y} \]

18674

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

18675

\[ {} y^{3}+y^{\prime } = 0 \]

18676

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

18677

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

18678

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

18679

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

18680

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \]

18681

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0 \]

18682

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

18683

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

18684

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

18685

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

18686

\[ {} y^{\prime } = -\frac {2 y+4 x}{2 x +3 y} \]

18687

\[ {} y^{\prime } = -\frac {4 x -2 y}{2 x -3 y} \]

18688

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

18689

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

18690

\[ {} 2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0 \]

18691

\[ {} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \]

18692

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

18693

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

18694

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

18695

\[ {} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0 \]

18696

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

18697

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

18698

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

18699

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

18700

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