4.27.7 Problems 601 to 700

Table 4.1565: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

7124

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

7286

\[ {} y^{\prime \prime }-4 y^{\prime } = 10 \]

7287

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

7288

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

7289

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

7290

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

7291

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]

7292

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

7293

\[ {} y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

7294

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

7295

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

7296

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

7297

\[ {} y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

7298

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

7299

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

7300

\[ {} 5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

7301

\[ {} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

7302

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

7303

\[ {} y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

7304

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

7305

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

7306

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

7307

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

7308

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

7309

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \]

7310

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

7311

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

7312

\[ {} y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \]

7313

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

7314

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

7315

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

7316

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \]

7317

\[ {} y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

7348

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

7355

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 26 \,{\mathrm e}^{3 x} \]

7356

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

7357

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 6 \,{\mathrm e}^{2 x} \]

7358

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

7362

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]

7369

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

7586

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

7587

\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (3 t \right ) \]

7588

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = -50 \sin \left (5 t \right ) \]

7589

\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \]

7590

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

7591

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y = \cos \left (\omega t \right ) \]

7592

\[ {} y^{\prime \prime }+25 y = \cos \left (\omega t \right ) \]

7681

\[ {} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

7682

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

7683

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

7684

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

7685

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

7766

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

7767

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

7768

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

7769

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

7770

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

7771

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \]

7772

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

7773

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

7774

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

7775

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

7776

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 100 \sin \left (4 x \right ) \]

7777

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

7778

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

7779

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

7780

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

7781

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

7782

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

7783

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

7784

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

7785

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

7786

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

7787

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

7788

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

7789

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

7790

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

7792

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

7793

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

7794

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

7795

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

7796

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

7797

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

7798

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

7800

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

7801

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

7805

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

7806

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

7807

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

7808

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

7809

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

7816

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

7817

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

7818

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

7822

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

7823

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

7824

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

7825

\[ {} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

7826

\[ {} y^{\prime \prime }-7 y^{\prime } = -3 \]

7834

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