4.5.13 Problems 1201 to 1300

Table 4.673: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

9467

\[ {} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

9615

\[ {} y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \]

9616

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

9617

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

9625

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

9626

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

9627

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

9630

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

9631

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \]

9637

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

9638

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

9639

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right ) \]

9640

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

9641

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \]

9644

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

9645

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

9646

\[ {} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

9647

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

9648

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

9649

\[ {} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \]

9650

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

9653

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

9654

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

9655

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

9656

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

9657

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

9658

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

9659

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

9660

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

9661

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]

9662

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

9664

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

9782

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

9783

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

9795

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

9800

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

9809

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

9810

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

9813

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

9814

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

9815

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

9816

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

9817

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

9818

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

9991

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

9992

\[ {} y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \]

9993

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

9994

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

10040

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

10041

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

10045

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

10053

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

10054

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

10055

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

10058

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

10060

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

10061

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

10062

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

10064

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

10065

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

10066

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

10067

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10089

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

10091

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

10092

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

10093

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

10094

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

10095

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

10096

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

10097

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

10098

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

10099

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

10100

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

10101

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

10102

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0 \]

10103

\[ {} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0 \]

10104

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

10105

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

10106

\[ {} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \]

10107

\[ {} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0 \]

10108

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

10109

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

10110

\[ {} y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \]

10111

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

10112

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

10113

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

10114

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

10115

\[ {} y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0 \]

10116

\[ {} y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0 \]

10117

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

10118

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

10119

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

10120

\[ {} y^{\prime \prime }-x y-x^{6}+64 = 0 \]

10121

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

10122

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

10123

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

10124

\[ {} y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

10125

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

10126

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