4.4.46 Problems 4501 to 4600

Table 4.635: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

20781

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

20782

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

20783

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

20786

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

20791

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

20813

\[ {} 2 y^{\prime \prime }+9 y^{\prime }-18 y = 0 \]

20874

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

20883

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

20884

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

20885

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

20889

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

20891

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

20892

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

20893

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

20894

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

20896

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

20897

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

20898

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

20899

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

20903

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

20905

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

20906

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

20907

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

20908

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

20911

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

20917

\[ {} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0 \]

20953

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]

20954

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

20955

\[ {} 8 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

20956

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

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

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

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

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

21029

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

21030

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

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

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

21272

\[ {} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5} = 0 \]

21273

\[ {} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x = 0 \]

21274

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

21276

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

21277

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

21278

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

21279

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

21280

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

21281

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

21282

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

21283

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

21284

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

21285

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

21286

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

21287

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

21290

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

21364

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

21370

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

21371

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

21372

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

21373

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

21374

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

21375

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

21376

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

21377

\[ {} x^{\prime \prime }+x+8 x^{7} = 0 \]

21378

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

21379

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

21380

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