4.1.78 Problems 7701 to 7800

Table 4.155: First order ode

#

ODE

Mathematica

Maple

Sympy

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

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

18701

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

18702

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

18703

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

18704

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

18705

\[ {} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0 \]

18706

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

18707

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

18708

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

18709

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

18710

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

18711

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

18712

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

18713

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

18714

\[ {} y^{\prime } = \frac {4 y-7 x}{5 x -y} \]

18715

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

18716

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

18717

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

18718

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

18719

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

18720

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

18721

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

18722

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

18723

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

18724

\[ {} 5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right ) \]

18725

\[ {} 3 t y^{\prime }+9 y = 2 t y^{{5}/{3}} \]

18726

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

18727

\[ {} y^{\prime } = r y-k^{2} y^{2} \]

18728

\[ {} y^{\prime } = a y+b y^{3} \]

18729

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

18730

\[ {} \left (3 x-y \right ) x^{\prime }+9 y -2 x = 0 \]

18731

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

18732

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

18733

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

18734

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

18735

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

18736

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

18737

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

18738

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

18739

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

18740

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

18741

\[ {} 4 y y^{\prime } x = 8 x^{2}+5 y^{2} \]

18742

\[ {} y^{\prime }+y-y^{{1}/{4}} = 0 \]

18830

\[ {} x^{\prime } = \frac {x \sqrt {6 x-9}}{3} \]

19177

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

19178

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

19180

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

19181

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

19182

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

19183

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

19184

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

19185

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

19186

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

19187

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

19188

\[ {} 3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime } \]

19189

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

19190

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