5.20.11 Problems 1001 to 1100

Table 5.927: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

3941

\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \]

3942

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

3943

\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \]

3944

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t} \]

3945

\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \]

3946

\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \]

3947

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

3948

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

3949

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

3950

\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \]

3951

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

3952

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

3953

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

3954

\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \]

3955

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

3963

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

3964

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

3965

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

3966

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

3967

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \]

3968

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t} \]

3969

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

3970

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \]

3977

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right ) \]

3978

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

3979

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

3980

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

3981

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

3982

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \]

3983

\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

3984

\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \]

3985

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \]

4118

\[ {}y^{\prime \prime }+8 y^{\prime }+15 y = 0 \]

4119

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

4120

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

4121

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

4122

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

4123

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

4124

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

4125

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

4126

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

4127

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

4128

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

4129

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

4130

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

4131

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

4132

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

4133

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

4134

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

4135

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

4136

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

4137

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

4138

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

4141

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

4142

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

4143

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

4144

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]

4145

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 0 \]

4146

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

4147

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

4148

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

4149

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

4150

\[ {}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

4151

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

4152

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

4153

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

4154

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

4155

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

4156

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

4157

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

4158

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \sin \left (x \right ) \]

4159

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \]

4160

\[ {}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \cos \left (2 x +3\right ) \]

4161

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

4162

\[ {}y^{\prime \prime }+9 y = 8 \sin \left (x \right ) \]

4163

\[ {}25 y^{\prime \prime }-30 y^{\prime }+9 y = 0 \]

4164

\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = \left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \]

4444

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

4445

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

4446

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

4447

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

4448

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

4449

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

4450

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

4451

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \]

4452

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

4453

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

4454

\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0 \]

4455

\[ {}y^{\left (6\right )}-64 y = 0 \]

4456

\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \]

4457

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \]

4458

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

4459

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

4460

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

4461

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

4462

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

4463

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

4464

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right ) \]

4465

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

4466

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime }+y = 9 \,{\mathrm e}^{2 x} \]