4.3.51 Problems 5001 to 5100

Table 4.385: Second order ode

#

ODE

Mathematica

Maple

Sympy

15548

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

15551

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

15552

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

15553

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

15555

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

15556

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

15559

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

15560

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

15562

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

15563

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

15565

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

15566

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

15567

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

15568

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

15569

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

15570

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

15571

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

15572

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

15573

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

15710

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

15714

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

15715

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

15716

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

15722

\[ {} y^{\prime \prime }-y^{\prime }-12 y = 0 \]

15723

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

15724

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

15725

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

15726

\[ {} y^{\prime \prime }-12 y^{\prime }+40 y = 0 \]

15729

\[ {} x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \]

15730

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \]

15751

\[ {} y^{\prime \prime }-y^{\prime }-12 y = 0 \]

15752

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

15755

\[ {} t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \]

15756

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \]

15764

\[ {} 16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \]

15773

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

15774

\[ {} y^{\prime \prime }-6 y^{\prime }+45 y = 0 \]

15775

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \]

15776

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

15777

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

15778

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

15786

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

15787

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

15930

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

16106

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

16107

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

16108

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

16109

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

16110

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

16111

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

16112

\[ {} 3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \]

16113

\[ {} t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \]

16114

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

16115

\[ {} y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

16116

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

16117

\[ {} y^{\prime \prime }+6 y^{\prime }+18 y = 0 \]

16118

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

16119

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

16120

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 0 \]

16121

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

16122

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = 0 \]

16123

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

16124

\[ {} y^{\prime \prime }+49 y = 0 \]

16125

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

16126

\[ {} t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0 \]

16127

\[ {} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \]

16128

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

16129

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

16130

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

16131

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \]

16132

\[ {} t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \]

16133

\[ {} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]

16134

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

16135

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

16136

\[ {} y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

16137

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

16138

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

16139

\[ {} y^{\prime \prime }+8 y^{\prime }+12 y = 0 \]

16140

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

16141

\[ {} 8 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

16142

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

16143

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

16144

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

16145

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

16146

\[ {} 4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \]

16147

\[ {} 7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

16148

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

16149

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

16150

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

16151

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

16152

\[ {} y^{\prime \prime }+y^{\prime }-12 y = 0 \]

16153

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

16154

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \]

16155

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

16156

\[ {} y^{\prime \prime }+36 y = 0 \]

16157

\[ {} y^{\prime \prime }+100 y = 0 \]

16158

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

16159

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

16160

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

16161

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]