4.3.54 Problems 5301 to 5400

Table 4.391: Second order ode

#

ODE

Mathematica

Maple

Sympy

16521

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

16522

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

16523

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \]

16524

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

16525

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

16526

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

16527

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

16528

\[ {} y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

16529

\[ {} y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

16530

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

16531

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

16532

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

16533

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

16534

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

16535

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

16536

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

16537

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

16538

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

16539

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

16540

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

16541

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

16542

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

16551

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

16552

\[ {} 4 x^{\prime \prime }+9 x = 0 \]

16553

\[ {} 9 x^{\prime \prime }+4 x = 0 \]

16554

\[ {} x^{\prime \prime }+64 x = 0 \]

16555

\[ {} x^{\prime \prime }+100 x = 0 \]

16556

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

16557

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

16558

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

16559

\[ {} x^{\prime \prime }+256 x = 0 \]

16560

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

16561

\[ {} 10 x^{\prime \prime }+\frac {x}{10} = 0 \]

16562

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

16563

\[ {} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]

16564

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

16565

\[ {} 4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]

16566

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

16567

\[ {} x^{\prime \prime }+4 x^{\prime }+20 x = 0 \]

16568

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

16569

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

16570

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]

16571

\[ {} x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

16572

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

16573

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

16574

\[ {} x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]

16575

\[ {} x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]

16576

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]

16589

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

16590

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

16591

\[ {} x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

16592

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

16835

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

16837

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

16838

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

16840

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

16841

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

16842

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

16843

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

16846

\[ {} y^{\prime \prime } \left (x +2\right )^{5} = 1 \]

16847

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

16848

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

16849

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

16850

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

16851

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

16852

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

16853

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

16855

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

16858

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

16859

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

16860

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

16861

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

16862

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

16863

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

16864

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

16865

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

16866

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

16868

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

16869

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

16870

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

16871

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

16872

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

16873

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

16874

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

16875

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

16876

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

16877

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

16878

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

16879

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

16881

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

16882

\[ {} 3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

16884

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

16885

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

16887

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

16889

\[ {} 4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

16892

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

16893

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

16903

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

16904

\[ {} y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2} \]

16905

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