4.4.47 Problems 4601 to 4700

Table 4.637: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

21381

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

21382

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

21391

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

21392

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

21393

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

21394

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

21395

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

21398

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

21414

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

21415

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

21416

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

21434

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

21435

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

21436

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

21437

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

21438

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

21439

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

21441

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

21442

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

21443

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

21444

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

21445

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

21575

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

21576

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

21590

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

21591

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

21593

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

21596

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

21597

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

21598

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

21599

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

21600

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

21601

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

21602

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

21603

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

21604

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

21605

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

21606

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

21607

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

21608

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

21609

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

21610

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

21611

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

21612

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

21613

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

21614

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

21615

\[ {} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25} = 0 \]

21679

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

21682

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

21684

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

21685

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

21687

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

21715

\[ {} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0 \]

21717

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

21718

\[ {} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0 \]

21720

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

21721

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

21727

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

21731

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

21732

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

21733

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

21735

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

21736

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

21740

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

21828

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

21829

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

21842

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

21843

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

21844

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

21845

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

21846

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

21850

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

21875

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

21876

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

21878

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

21879

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

21880

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

21903

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

21904

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

21908

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

21990

\[ {} y^{\prime \prime }-12 y^{\prime }+35 y = 0 \]

21991

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

21992

\[ {} 9 y^{\prime \prime }-30 y^{\prime }+25 y = 0 \]

21993

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

22025

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

22026

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

22027

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

22028

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

22029

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

22038

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

22047

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

22048

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

22051

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

22054

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

22062

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

22070

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

22074

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

22078

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

22080

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

22083

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