4.27.6 Problems 501 to 600

Table 4.1563: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

4521

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t} \]

4522

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \]

4523

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

4524

\[ {} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \]

4525

\[ {} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \]

4526

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

4527

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

4528

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

5716

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

5717

\[ {} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \]

5718

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

5719

\[ {} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \]

5722

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

5723

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

5724

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

5725

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

5726

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

5727

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

5728

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

5729

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

5730

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

5731

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

5732

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

5733

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

5734

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

5736

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

5738

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

5739

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

5740

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

5741

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

5742

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

5743

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

5744

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

5745

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

5746

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

5774

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

5775

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

5776

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

5777

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

5778

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

5779

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 8 x^{2} {\mathrm e}^{3 x} \]

5780

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right ) \]

5782

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

5784

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right ) \]

5786

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

5788

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

5789

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

5790

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

5791

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

5793

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right ) \]

5795

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

5797

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

5800

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 4 x^{2} {\mathrm e}^{x} \]

5801

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

5803

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \cosh \left (x \right ) {\mathrm e}^{-3 x} \]

5805

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

5807

\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \]

5809

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{3 x} \]

5811

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

5812

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

5815

\[ {} b y+a y^{\prime }+y^{\prime \prime } = f \left (x \right ) \]

7085

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

7086

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

7087

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

7088

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

7089

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

7090

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

7091

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

7092

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

7093

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

7094

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

7095

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

7096

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

7097

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

7098

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

7099

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

7100

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

7101

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

7102

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

7103

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

7104

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

7105

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]

7106

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

7107

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

7108

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \left (2 x -3\right ) \]

7109

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

7110

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

7111

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

7112

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

7113

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

7114

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

7115

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]

7116

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

7117

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

7118

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

7119

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

7120

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

7121

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

7122

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

7123

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