3.1.37 Problems 3601 to 3700

Table 3.73: First order ode

#

ODE

Mathematica

Maple

7346

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

7347

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

7348

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

7349

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

7350

\[ {}\pi y^{\prime } = 0 \]

7351

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

7352

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

7353

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

7354

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

7355

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

7356

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

7357

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

7358

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

7359

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

7360

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

7361

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

7362

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

7363

\[ {}{y^{\prime }}^{n} = 0 \]

7364

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

7365

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

7366

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

7367

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

7368

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

7369

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

7370

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

7371

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

7372

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

7373

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

7374

\[ {}{y^{\prime }}^{4} = \frac {1}{x y^{3}} \]

7375

\[ {}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}} \]

7376

\[ {}y^{\prime } = \sqrt {1+6 x +y} \]

7377

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

7378

\[ {}y^{\prime } = \left (1+6 x +y\right )^{\frac {1}{4}} \]

7379

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

7380

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

7381

\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]

7382

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

7383

\[ {}y^{\prime } = 10+{\mathrm e}^{x +y} \]

7384

\[ {}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2} \]

7385

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

7386

\[ {}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \]

7448

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

7480

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

7481

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

7482

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

7489

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

8338

\[ {}y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}} = 0 \]

8339

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

8340

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

8341

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

8342

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

8343

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

8344

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

8345

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

8346

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

8347

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

8348

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

8349

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

8350

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

8351

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

8352

\[ {}y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1 = 0 \]

8353

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

8354

\[ {}y^{\prime }-y^{2}-3 y+4 = 0 \]

8355

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

8356

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

8357

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

8358

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

8359

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

8360

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

8361

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

8362

\[ {}y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1} = 0 \]

8363

\[ {}y^{\prime }-\left (y A -a \right ) \left (B y-b \right ) = 0 \]

8364

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

8365

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

8366

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

8367

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

8368

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

8369

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

8370

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

8371

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

8372

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

8373

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

8374

\[ {}y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2} = 0 \]

8375

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

8376

\[ {}y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0} = 0 \]

8377

\[ {}y^{\prime }+3 a y^{3}+6 a x y^{2} = 0 \]

8378

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

8379

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

8380

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

8381

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

8382

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

8383

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-1-a} = 0 \]

8384

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

8385

\[ {}y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2} = 0 \]

8387

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

8388

\[ {}y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

8389

\[ {}y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}} = 0 \]

8390

\[ {}y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \]

8391

\[ {}y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0 \]

8392

\[ {}y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0 \]