4.3.75 Problems 7401 to 7500

Table 4.513: Second order ode

#

ODE

Mathematica

Maple

Sympy

20957

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

20958

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

20959

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

20960

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

20961

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

20962

\[ {} x^{\prime \prime }-3 x^{\prime }+2 x = 6 \,{\mathrm e}^{3 t} \]

20963

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 10 \]

20964

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 5+10 \sin \left (2 x \right ) \]

20965

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 3 \,{\mathrm e}^{x} \]

20966

\[ {} y^{\prime \prime }+5 y^{\prime }-6 y = 3 \,{\mathrm e}^{x} \]

20967

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

20968

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

20969

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

20970

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

20971

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 6 x \,{\mathrm e}^{2 x} \]

20972

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

20973

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

20974

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

20975

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

20976

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

20977

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

20978

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

20979

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

20980

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]

20981

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

20983

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

20984

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

20985

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 2 x^{3} \]

20986

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 5 x^{2} \]

20987

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 20 \,{\mathrm e}^{-2 x} \]

20988

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

20989

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

20990

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

20991

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

20992

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

20993

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

20994

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

20995

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

20996

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-15 y = x^{4} {\mathrm e}^{x} \]

21029

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

21030

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

21031

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

21032

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

21033

\[ {} y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{t} \]

21034

\[ {} y^{\prime \prime }+4 y = \delta \left (t -1\right ) \]

21035

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right ) \]

21036

\[ {} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right ) \]

21114

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

21115

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

21116

\[ {} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u = c \cos \left (\omega t \right ) \]

21118

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

21220

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

21221

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

21222

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

21223

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

21224

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

21225

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

21226

\[ {} x^{\prime \prime }+8 x^{\prime }+16 x = 0 \]

21227

\[ {} x^{\prime \prime }+2 x^{\prime }-15 x = 0 \]

21228

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

21229

\[ {} 4 x^{\prime }+2 x^{\prime \prime } = -5 x \]

21230

\[ {} x^{\prime \prime }-6 x^{\prime }+9 x = 0 \]

21231

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

21232

\[ {} x^{\prime \prime }+4 x^{\prime }+k x = 0 \]

21233

\[ {} x^{\prime \prime }+b x^{\prime }+c x = 0 \]

21234

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = 0 \]

21235

\[ {} x^{\prime \prime }+p x^{\prime } = 0 \]

21236

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

21237

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

21238

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

21239

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

21240

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

21241

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

21242

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

21243

\[ {} x^{\prime \prime }-2 x^{\prime }+5 x = 0 \]

21244

\[ {} x^{\prime \prime }-2 x^{\prime }+5 x = 0 \]

21245

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

21246

\[ {} x^{\prime \prime }-4 x = t \]

21247

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

21248

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

21249

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

21250

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

21251

\[ {} x^{\prime \prime }-x = 3 \,{\mathrm e}^{2 t} \]

21252

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

21253

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

21254

\[ {} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t} \]

21255

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

21256

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

21257

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

21258

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

21259

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

21260

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

21261

\[ {} x^{\prime \prime }-x = {\mathrm e}^{k t} \]

21262

\[ {} x^{\prime \prime }-x^{\prime }-2 x = 3 \,{\mathrm e}^{-t} \]

21263

\[ {} x^{\prime \prime }-3 x^{\prime }+2 x = 3 t \,{\mathrm e}^{t} \]

21264

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \]

21265

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

21266

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

21267

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

21268

\[ {} x^{\prime \prime }+9 x = \sin \left (t \right )+\sin \left (3 t \right ) \]