4.5.2 Problems 101 to 200

Table 4.651: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

571

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

572

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

573

\[ {} x^{\prime \prime }+6 x^{\prime }+9 x = f \left (t \right ) \]

574

\[ {} x^{\prime \prime }+6 x^{\prime }+8 x = f \left (t \right ) \]

575

\[ {} x^{\prime \prime }+4 x^{\prime }+8 x = f \left (t \right ) \]

838

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

839

\[ {} y^{\prime \prime }-4 y = 12 \]

840

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 \]

841

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

842

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

843

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

844

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

869

\[ {} y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

870

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

871

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

872

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \]

873

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

874

\[ {} 2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \]

875

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

876

\[ {} y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \]

877

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \]

878

\[ {} y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \]

879

\[ {} y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

880

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

881

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

882

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

883

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \]

884

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

885

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

886

\[ {} y^{\prime \prime }+9 y = \sin \left (2 x \right ) \]

887

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

888

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

889

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

890

\[ {} y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

891

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

892

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

893

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \]

894

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

895

\[ {} y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \]

896

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

897

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

898

\[ {} y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \]

899

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

900

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

901

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

902

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

903

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \]

904

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

905

\[ {} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}} \]

906

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

907

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

908

\[ {} x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]

909

\[ {} x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]

910

\[ {} x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]

911

\[ {} x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]

912

\[ {} m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]

913

\[ {} x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

914

\[ {} x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

915

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

916

\[ {} x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

917

\[ {} x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]

918

\[ {} x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

919

\[ {} x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

920

\[ {} x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]

921

\[ {} x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \]

1333

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \]

1334

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

1335

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

1336

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

1337

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

1338

\[ {} y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \]

1339

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}} \]

1340

\[ {} y^{\prime \prime }+4 y = 3 \csc \left (2 t \right ) \]

1341

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

1342

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \]

1343

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \]

1344

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

1345

\[ {} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

1346

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

1347

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

1348

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

1349

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

1350

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

1351

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

1352

\[ {} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \]

1353

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

1354

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

1357

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \]

1358

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \]

1359

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \]

1360

\[ {} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \]

1490

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

1491

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

1492

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

1493

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \]

1494

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

1495

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \]

1496

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \]

1497

\[ {} y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \]

1498

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \]