4.2.69 Problems 6801 to 6900

Table 4.343: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

22432

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 0 \]

22443

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

22447

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

22450

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

22473

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

22575

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

22593

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

22597

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

22598

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

22601

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

22602

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

22603

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

22607

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

22658

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

22690

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

22706

\[ {} u^{\prime \prime }+\frac {u^{\prime }}{r} = 4-4 r \]

22729

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

22731

\[ {} s^{\prime \prime }+b s^{\prime }+\omega ^{2} s = 0 \]

22732

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

22733

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

22734

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

22736

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

22737

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

22738

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

22739

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

22740

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

22742

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

22743

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

22744

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

22745

\[ {} 4 y^{\prime \prime }-25 y = 0 \]

22746

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

22748

\[ {} i^{\prime \prime }-4 i^{\prime }+2 i = 0 \]

22750

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

22751

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

22754

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

22755

\[ {} y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y = 0 \]

22758

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

22759

\[ {} 16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

22760

\[ {} 4 i^{\prime \prime }-12 i^{\prime }+9 i = 0 \]

22764

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

22766

\[ {} s^{\prime \prime }+16 s^{\prime }+64 s = 0 \]

22767

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

22768

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

22769

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

22770

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

22771

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

22772

\[ {} 4 y^{\prime \prime }+9 y = 0 \]

22773

\[ {} 4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

22776

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

22777

\[ {} u^{\prime \prime }+16 u = 0 \]

22778

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

22784

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

22792

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

22793

\[ {} y^{\prime \prime }+2 y^{\prime }-3 y = 0 \]

22794

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

22797

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

22798

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0 \]

22799

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

22800

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

22801

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

22802

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

22803

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

22804

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

22805

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

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

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

22833

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

22834

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

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

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

22846

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

22847

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