4.1.43 Problems 4201 to 4300

Table 4.85: First order ode

#

ODE

Mathematica

Maple

Sympy

9840

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

9841

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

9842

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

9983

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

9984

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

9985

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

9986

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

9987

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

9988

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

9989

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

9990

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

9999

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

10000

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

10001

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

10002

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

10003

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

10004

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

10005

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

10006

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

10007

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

10008

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

10009

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

10010

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

10011

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

10012

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

10013

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

10014

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

10015

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

10016

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

10017

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

10018

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

10019

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

10020

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

10021

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

10022

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

10023

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

10024

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

10025

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

10026

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

10027

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

10028

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

10029

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

10030

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

10031

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

10032

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

10033

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

10034

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

10035

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

10036

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

10037

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

10042

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

10043

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

10044

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

10056

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

10057

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

10075

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

10076

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

10077

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

10078

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

10079

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

10080

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

10082

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

10083

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

10084

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

10090

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

10146

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

10172

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

10173

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

10175

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

10207

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

10208

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

10238

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

10262

\[ {} h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}} = b^{2} \]

10266

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

10268

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

10270

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

10271

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

10272

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

10273

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

10274

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

10275

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

10276

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

10277

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

10278

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

10279

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

10280

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

10281

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

10282

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

10283

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

10284

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

10285

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

10286

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

10287

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

10288

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

10289

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

10290

\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r} \]

10291

\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r x} \]

10292

\[ {} c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}} \]

10293

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

10294

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