4.4.44 Problems 4301 to 4400

Table 4.631: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

19591

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

19592

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

19593

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

19594

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

19595

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

19596

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

19597

\[ {} y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]

19598

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

19599

\[ {} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

19600

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

19601

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

19602

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

19603

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]

19604

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

19605

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

19606

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

19607

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

19608

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

19700

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

19739

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

19743

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

19744

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0 \]

19746

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

19773

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

19799

\[ {} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

19802

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

19803

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

19804

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

19805

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

19806

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

19807

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

19808

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

19809

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

19810

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

19817

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

19819

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

19820

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

19822

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

19824

\[ {} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \]

19851

\[ {} \theta ^{\prime \prime } = -p^{2} \theta \]

19853

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

19854

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

19866

\[ {} \theta ^{\prime \prime }-p^{2} \theta = 0 \]

19867

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

19868

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

19869

\[ {} r^{\prime \prime }-a^{2} r = 0 \]

19882

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

19883

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

19885

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

19888

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

19894

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

19895

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

19896

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

19897

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

19899

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

19901

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

19902

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

19904

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

19940

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

19941

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

19968

\[ {} e y^{\prime \prime } = P \left (a -y\right ) \]

19979

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

19985

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

19986

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

19987

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

19994

\[ {} V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0 \]

19995

\[ {} V^{\prime \prime }+\frac {V^{\prime }}{r} = 0 \]

20009

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

20010

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

20011

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

20152

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

20153

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

20154

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

20155

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

20158

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

20216

\[ {} \left (2 x +5\right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0 \]

20217

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

20234

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

20237

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

20238

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

20242

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

20243

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

20244

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

20245

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

20247

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

20250

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

20252

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

20253

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

20258

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

20259

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

20267

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

20272

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

20274

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

20276

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

20279

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

20283

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

20284

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

20290

\[ {} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

20291

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

20292

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