4.27.22 Problems 2101 to 2200

Table 4.1595: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

22265

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

22268

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

22269

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

22270

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

22274

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

22275

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

22276

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

22278

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

22279

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

22281

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

22282

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

22283

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

22285

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

22349

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

22350

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

22351

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

22352

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

22353

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

22361

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

22362

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

22363

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

22364

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

22365

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

22366

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 t} \]

22367

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (t -4\right ) \]

22397

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

22399

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

22404

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

22405

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

22407

\[ {} y^{\prime \prime }-4 y^{\prime }-5 y = {\mathrm e}^{3 x} \]

22410

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

22414

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 6 \,{\mathrm e}^{x} \]

22422

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

22424

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

22426

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

22427

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

22443

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

22447

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

22593

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

22597

\[ {} i^{\prime \prime } = t^{2}+1 \]

22658

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

22729

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

22733

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

22734

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

22737

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

22739

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

22740

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

22742

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

22802

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

22803

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

22804

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

22805

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x}+15 x \]

22806

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

22808

\[ {} y^{\prime \prime }+16 y = 5 \sin \left (x \right ) \]

22809

\[ {} s^{\prime \prime }-3 s^{\prime }+2 s = 8 t^{2}+12 \,{\mathrm e}^{-t} \]

22810

\[ {} y^{\prime \prime }+y = 6 \cos \left (x \right )^{2} \]

22811

\[ {} L q^{\prime \prime }+R q^{\prime }+\frac {q}{c} = E_{0} \sin \left (\omega t \right ) \]

22812

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

22813

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

22814

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

22815

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

22816

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

22817

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

22818

\[ {} y^{\prime \prime }+4 y = 8 \cos \left (2 x \right )-4 x \]

22820

\[ {} i^{\prime \prime }+9 i = 12 \cos \left (3 t \right ) \]

22821

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

22823

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

22824

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

22825

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

22826

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

22827

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

22829

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

22830

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

22831

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

22832

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

22833

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

22834

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

22835

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

22837

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

22838

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

22839

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

22841

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

22842

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

22843

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

22844

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

22845

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

22846

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

22847

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

22848

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

22849

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

22850

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

22851

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

22855

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

22856

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

22857

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

22858

\[ {} -y+y^{\prime \prime } = 2 x^{4}-3 x +1 \]

22859

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

22860

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

22861

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

22863

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