4.20.20 Problems 1901 to 2000

Table 4.1237: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

9333

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

9334

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

9335

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

9336

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

9337

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

9338

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

9339

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

9340

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

9341

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

9342

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

9343

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

9344

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

9345

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

9346

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

9348

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

9349

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

9350

\[ {} y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \]

9351

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

9352

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

9354

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

9356

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

9453

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \]

9454

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

9455

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

9459

\[ {} y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

9460

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

9461

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

9462

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

9463

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

9464

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

9465

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

9466

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

9467

\[ {} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

9505

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

9507

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

9509

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

9511

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

9593

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

9614

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

9615

\[ {} y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \]

9616

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

9617

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

9618

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

9619

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

9621

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

9624

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

9625

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

9626

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

9627

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

9628

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

9629

\[ {} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

9630

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

9631

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]

9632

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

9633

\[ {} y^{\prime \prime }+8 y^{\prime }+20 y = 0 \]

9637

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

9638

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

9639

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right ) \]

9640

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

9641

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \]

9644

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

9645

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

9646

\[ {} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

9647

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

9650

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

9653

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

9654

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

9655

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

9656

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

9657

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

9658

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

9659

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \]

9660

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

9661

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]

9662

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

9663

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

9664

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \]

9786

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

9815

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

9816

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

9817

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \]

9818

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \]

9991

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

9992

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

9993

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

9994

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

10038

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

10039

\[ {} 5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]

10040

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

10041

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

10052

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

10053

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

10054

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

10055

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

10058

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

10059

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

10063

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

10068

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10086

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