3.9.30 Problems 2901 to 3000

Table 3.565: First order ode linear in derivative

#

ODE

Mathematica

Maple

6263

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

6264

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

6401

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

6405

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

6407

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

6409

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

6411

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

6413

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

6415

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

6417

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

6419

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

6421

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

6422

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

6426

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

6502

\[ {}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right ) \]

6503

\[ {}L i^{\prime }+R i = E_{0} \delta \left (t \right ) \]

6504

\[ {}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \]

6545

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

6547

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

6549

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

6656

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

6657

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

6658

\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \]

6659

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

6666

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

6668

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

6669

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

6680

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \]

6681

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

6682

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

6688

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

6689

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

6697

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

6698

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

7029

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

7030

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

7031

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

7032

\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \]

7033

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

7034

\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \]

7035

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

7036

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

7045

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

7046

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

7047

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

7048

\[ {}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \]

7049

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

7050

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

7051

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

7052

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

7053

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

7054

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

7055

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

7056

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

7057

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

7058

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

7059

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

7060

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

7062

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

7063

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

7064

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

7065

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

7066

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

7068

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

7069

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

7070

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

7071

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

7072

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

7074

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

7075

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

7076

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

7077

\[ {}p^{\prime } = a p-b p^{2} \]

7078

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

7080

\[ {}x y^{\prime }-2 y+b y^{2} = c \,x^{4} \]

7081

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

7082

\[ {}u^{\prime }+u^{2} = \frac {1}{x^{\frac {4}{5}}} \]

7083

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

7090

\[ {}f^{\prime } = \frac {1}{f} \]

7102

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

7103

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

7121

\[ {}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{\frac {3}{4}}-3 k x \]

7124

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

7125

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

7126

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

7128

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

7129

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

7130

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

7136

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

7192

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]

7218

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

7219

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

7221

\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]

7284

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

7312

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

7314

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

7316

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

7317

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

7318

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

7319

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

7320

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