4.1.39 Problems 3801 to 3900

Table 4.77: First order ode

#

ODE

Mathematica

Maple

Sympy

7737

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

7738

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

7739

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

7740

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

7741

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

7742

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

7743

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

7744

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

7745

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

7746

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

7747

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

7748

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

7749

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

7750

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

7751

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

7752

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

7753

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

7754

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

7755

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

7756

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

7757

\[ {} 5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0 \]

7758

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

7773

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

7774

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

7775

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

7776

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

7779

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

7780

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

7781

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

7782

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

7783

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

7784

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

7785

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

7786

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

7787

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

7788

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

7789

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

7790

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

7791

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

7792

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

7793

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

7794

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

7795

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

7796

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

7797

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

7798

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

7799

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

7800

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

7801

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

7802

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

7803

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

7805

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

7807

\[ {} x^{5} y^{\prime }+y^{5} = 0 \]

7808

\[ {} y^{\prime } = 4 x y \]

7809

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

7810

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

7811

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

7812

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

7813

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

7814

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

7815

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

7816

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

7817

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

7818

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

7819

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

7820

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

7821

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

7822

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

7825

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

7826

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

7827

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

7828

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

7829

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

7830

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

7831

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

7832

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

7833

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

7834

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

7835

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

7836

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

7837

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

7838

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

7839

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

7840

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

7841

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

7842

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

7843

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

7844

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

7845

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

7846

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

7847

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

7848

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

7849

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

7850

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

7851

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

7852

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

7853

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

7854

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

7855

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

7856

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