3.9.58 Problems 5701 to 5800

Table 3.621: First order ode linear in derivative

#

ODE

Mathematica

Maple

14407

\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

14408

\[ {}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \]

14409

\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \]

14410

\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \]

14411

\[ {}y^{\prime }+3 y = -10 \sin \left (t \right ) \]

14412

\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \]

14413

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

14414

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

14415

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

14416

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

14417

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

14418

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

14419

\[ {}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \]

14420

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

14421

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

14422

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

14423

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

14424

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

14425

\[ {}t r^{\prime }+r = t \cos \left (t \right ) \]

14426

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

14427

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

14429

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

14432

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

14433

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

14434

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

14435

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

14436

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

14437

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

14438

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

14439

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

14440

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

14441

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

14442

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

14443

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

14444

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

14568

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

14569

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

14570

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

14571

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

14572

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

14934

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

14935

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

14936

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

14937

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

14938

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

14939

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

14940

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

14941

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

14942

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

14943

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

14944

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

14945

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

14946

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

14947

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

14948

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

14949

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

14950

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

14951

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

14952

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

14953

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

14954

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

14955

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

14956

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

14957

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

14958

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

14959

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

14960

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

14961

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

14962

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

14963

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

14964

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

14965

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

14966

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

14967

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

14968

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

14969

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

14970

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

14971

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

14972

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

14973

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

14974

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

14975

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

14976

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

14977

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

14978

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

14979

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

14980

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

14981

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

14982

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

14983

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

14984

\[ {}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0 \]

14985

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

14986

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

14987

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

14988

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

14989

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

14990

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

14991

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

14999

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

15000

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