4.27.15 Problems 1401 to 1500

Table 4.1581: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

16882

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

16883

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \]

16887

\[ {} y^{\prime \prime }+9 y = 27 t^{3} \]

16888

\[ {} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]

16890

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t} \]

16893

\[ {} y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right ) \]

16894

\[ {} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]

16895

\[ {} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]

16896

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

16897

\[ {} y^{\prime \prime }+4 y = 1 \]

16898

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

16899

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

16900

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

16901

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

16902

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]

16903

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

16904

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]

16905

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]

16906

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]

16909

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

16910

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

16911

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]

16913

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

16914

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

16917

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

16918

\[ {} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right ) \]

16920

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

16921

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

16923

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

16924

\[ {} y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right ) \]

16925

\[ {} y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]

16926

\[ {} y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]

16927

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

16928

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]

16929

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]

16930

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]

16931

\[ {} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]

17068

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

17083

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

17135

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

17136

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = 2 \]

17144

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

17472

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

17538

\[ {} y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \]

17539

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \]

17540

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

17541

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

17542

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

17543

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

17544

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

17545

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

17546

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

17547

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

17548

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

17549

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \]

17550

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

17551

\[ {} 5 y^{\prime \prime }+y^{\prime }-4 y = -3 \]

17552

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

17553

\[ {} 16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

17554

\[ {} y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

17555

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

17556

\[ {} 8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

17557

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

17558

\[ {} y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

17559

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

17560

\[ {} y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

17561

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

17562

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

17563

\[ {} y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

17564

\[ {} y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

17565

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

17566

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

17567

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

17568

\[ {} y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

17569

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

17570

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

17571

\[ {} y^{\prime \prime }+3 y^{\prime } = 18 \]

17572

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

17573

\[ {} y^{\prime \prime }-4 y = 32 t \]

17574

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

17575

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

17576

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 4 \]

17577

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \]

17578

\[ {} y^{\prime \prime }+6 y^{\prime }+25 y = -1 \]

17579

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

17580

\[ {} y^{\prime \prime }-y^{\prime } = -3 t -4 \,{\mathrm e}^{2 t} t^{2} \]

17581

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

17582

\[ {} y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

17583

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

17584

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

17585

\[ {} y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

17586

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

17592

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

17593

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

17594

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \]

17595

\[ {} y^{\prime \prime }+4 y = 1 \]

17596

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

17597

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \]

17598

\[ {} y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \]

17599

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \]