4.1.69 Problems 6801 to 6900

Table 4.137: First order ode

#

ODE

Mathematica

Maple

Sympy

15116

\[ {} y^{2}+1-y^{\prime } = 0 \]

15117

\[ {} y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \]

15118

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

15119

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

15120

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

15121

\[ {} y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \]

15122

\[ {} 2 y-6 x +\left (1+x \right ) y^{\prime } = 0 \]

15123

\[ {} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \]

15124

\[ {} y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \]

15125

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

15126

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

15127

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

15128

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

15129

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

15130

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

15131

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

15132

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

15133

\[ {} y^{\prime } = \tan \left (6 x +3 y+1\right )-2 \]

15134

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

15135

\[ {} y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \]

15136

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

15137

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

15195

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

15514

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

15515

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

15516

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

15549

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

15550

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

15554

\[ {} y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15557

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

15558

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

15561

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

15564

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

15711

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

15713

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

15717

\[ {} 2 x -1-y^{\prime } = 0 \]

15718

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

15719

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

15720

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

15721

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

15731

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

15732

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

15733

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

15734

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

15735

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

15736

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

15737

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

15738

\[ {} y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

15739

\[ {} y^{\prime } = \frac {1}{x \ln \left (x \right )} \]

15740

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

15741

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

15742

\[ {} y^{\prime } = \frac {-2 x -10}{\left (x +2\right ) \left (-4+x \right )} \]

15743

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

15744

\[ {} y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \]

15745

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

15746

\[ {} y^{\prime } = \frac {1}{x^{2}-16} \]

15747

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

15748

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

15749

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

15750

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

15757

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

15758

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

15759

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

15760

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

15761

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

15762

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

15763

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

15766

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

15767

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

15771

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

15772

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

15779

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

15780

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

15781

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

15782

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

15783

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

15784

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

15785

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

15788

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

15789

\[ {} y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \]

15790

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

15791

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

15792

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

15793

\[ {} y^{\prime } = y^{{1}/{5}} \]

15794

\[ {} \frac {y^{\prime }}{t} = \sqrt {y} \]

15795

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

15796

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

15797

\[ {} y^{\prime } = 6 y^{{2}/{3}} \]

15798

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

15799

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

15800

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

15801

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

15802

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

15803

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

15804

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

15805

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

15806

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

15807

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

15808

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

15809

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