6.251 Problems 25001 to 25100

Table 6.501: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

25001

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

25002

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

25003

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

25004

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

25005

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

25006

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

25007

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

25008

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

25009

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

25010

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

25011

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

25012

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

25013

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

25014

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

25015

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

25016

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

25017

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

25018

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

25019

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

25020

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

25021

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

25022

\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

25023

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

25024

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

25025

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

25026

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

25027

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

25028

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

25029

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

25030

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

25031

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

25032

\[ {} y^{\prime } = 3 y+12 \]

25033

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

25034

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

25035

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

25036

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

25037

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

25038

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

25039

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

25040

\[ {} y^{\prime } = {\mathrm e}^{2 t}-1 \]

25041

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

25042

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

25043

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

25044

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25045

\[ {} y^{\prime } = 3 y+12 \]

25046

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

25047

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

25048

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

25049

\[ {} y^{\prime } = {\mathrm e}^{2 t}-1 \]

25050

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

25051

\[ {} y^{\prime \prime } = 6 \sin \left (3 t \right ) \]

25052

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

25053

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

25054

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

25055

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

25056

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

25057

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

25058

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

25059

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

25060

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

25061

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

25062

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

25063

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

25064

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

25065

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

25066

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

25067

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

25068

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

25069

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

25070

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

25071

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

25072

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

25073

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

25074

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

25075

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

25076

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

25077

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

25078

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

25079

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

25080

\[ {} y^{\prime } = t^{m} y^{n} \]

25081

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

25082

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

25083

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

25084

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

25085

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

25086

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

25087

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

25088

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

25089

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

25090

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

25091

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

25092

\[ {} y^{\prime } = \frac {\cot \left (y\right )}{t} \]

25093

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

25094

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

25095

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

25096

\[ {} 3 y+y^{\prime } = {\mathrm e}^{t} \]

25097

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

25098

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

25099

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

25100

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