Number of problems in this table is 66
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# |
ODE |
CAS classification |
Program classification |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) f \left (t \right )+y \left (t \right ) g \left (t \right ) \\ y^{\prime }\left (t \right )=-x \left (t \right ) g \left (t \right )+y \left (t \right ) f \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right )=g \left (t \right ) \\ y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right )=h \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \cos \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right ) {\mathrm e}^{-\sin \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+y \left (t \right )=0 \\ t y^{\prime }\left (t \right )+x \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=t \\ t y^{\prime }\left (t \right )-\left (2+t \right ) x \left (t \right )-t y \left (t \right )=-t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )-2 y \left (t \right )=t \\ t y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right )=t^{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }\left (t \right )=t \left (1-2 \sin \left (t \right )\right ) x \left (t \right )+y \left (t \right ) t^{2} \\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }\left (t \right )=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x \left (t \right )+t \left (1-t \cos \left (t \right )\right ) y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right )=f \left (t \right ) \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )=g \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right )={\mathrm e}^{2 t} \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+x \left (t \right )=2 t \\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-9 x \left (t \right )+3 y \left (t \right )=\sin \left (2 t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )=0 \\ x^{\prime \prime }\left (t \right )-2 y^{\prime }\left (t \right )=2 t -\cos \left (2 t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )-t y^{\prime }\left (t \right )-2 y \left (t \right )=0 \\ t x^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )+x \left (t \right ) t =0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )-a^{2} y \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a x \left (t \right )+b y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=c x \left (t \right )+d y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1} \\ y^{\prime \prime }\left (t \right )=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right )=-5 \\ y^{\prime \prime }\left (t \right )-4 x \left (t \right )-3 y \left (t \right )=-3 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+6 x \left (t \right )+7 y \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right )=2 t \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-a y^{\prime }\left (t \right )+b x \left (t \right )=0 \\ y^{\prime \prime }\left (t \right )+a x^{\prime }\left (t \right )+b y \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} a_{1} x^{\prime \prime }\left (t \right )+b_{1} x^{\prime }\left (t \right )+c_{1} x \left (t \right )-A y^{\prime }\left (t \right )=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }\left (t \right )+b_{2} y^{\prime }\left (t \right )+c_{2} y \left (t \right )+A x^{\prime }\left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+a \left (x^{\prime }\left (t \right )-y^{\prime }\left (t \right )\right )+b_{1} x \left (t \right )=c_{1} {\mathrm e}^{i \omega t} \\ y^{\prime \prime }\left (t \right )+a \left (y^{\prime }\left (t \right )-x^{\prime }\left (t \right )\right )+b_{2} y \left (t \right )=c_{2} {\mathrm e}^{i \omega t} \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} \operatorname {a11} x^{\prime \prime }\left (t \right )+\operatorname {b11} x^{\prime }\left (t \right )+\operatorname {c11} x \left (t \right )+\operatorname {a12} y^{\prime \prime }\left (t \right )+\operatorname {b12} y^{\prime }\left (t \right )+\operatorname {c12} y \left (t \right )=0 \\ \operatorname {a21} x^{\prime \prime }\left (t \right )+\operatorname {b21} x^{\prime }\left (t \right )+\operatorname {c21} x \left (t \right )+\operatorname {a22} y^{\prime \prime }\left (t \right )+\operatorname {b22} y^{\prime }\left (t \right )+\operatorname {c22} y \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right )=0 \\ y^{\prime \prime \prime }\left (t \right )-y^{\prime \prime }\left (t \right )+2 x^{\prime }\left (t \right )-x \left (t \right )=t \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )=\sinh \left (2 t \right ) \\ 2 x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )=2 t \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )-x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=0 \\ x^{\prime \prime }\left (t \right )+y^{\prime \prime }\left (t \right )-x \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )=2 x \left (t \right )-t \\ t^{3} y^{\prime }\left (t \right )=-x \left (t \right )+y \left (t \right ) t^{2}+t \\ t^{4} z^{\prime }\left (t \right )=-x \left (t \right )-y \left (t \right ) t^{2}+t^{3} z \left (t \right )+t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} a t x^{\prime }\left (t \right )=b c \left (y \left (t \right )-z \left (t \right )\right ) \\ b t y^{\prime }\left (t \right )=c a \left (-x \left (t \right )+z \left (t \right )\right ) \\ c t z^{\prime }\left (t \right )=a b \left (x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=a x_{2} \left (t \right )+b x_{3} \left (t \right ) \cos \left (c t \right )+b x_{4} \left (t \right ) \sin \left (c t \right ) \\ x_{2}^{\prime }\left (t \right )=-a x_{1} \left (t \right )+b x_{3} \left (t \right ) \sin \left (c t \right )-b x_{4} \left (t \right ) \cos \left (c t \right ) \\ x_{3}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \cos \left (c t \right )-b x_{2} \left (t \right ) \sin \left (c t \right )+a x_{4} \left (t \right ) \\ x_{4}^{\prime }\left (t \right )=-b x_{1} \left (t \right ) \sin \left (c t \right )+b x_{2} \left (t \right ) \cos \left (c t \right )-a x_{3} \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-x \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=y \left (t \right ) \left (x \left (t \right )+y \left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\left (a y \left (t \right )+b \right ) x \left (t \right ) \\ y^{\prime }\left (t \right )=\left (c x \left (t \right )+d \right ) y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=h \left (a -x \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=k \left (b -y \left (t \right )\right ) \left (c -x \left (t \right )-y \left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )^{2}-\cos \left (x \left (t \right )\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \sin \left (x \left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} \left (t^{2}+1\right ) x^{\prime }\left (t \right )=-x \left (t \right ) t +y \left (t \right ) \\ \left (t^{2}+1\right ) y^{\prime }\left (t \right )=-x \left (t \right )-t y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) x^{\prime }\left (t \right )=-2 x \left (t \right ) t \\ \left (x \left (t \right )^{2}+y \left (t \right )^{2}-t^{2}\right ) y^{\prime }\left (t \right )=-2 t y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} {x^{\prime }\left (t \right )}^{2}+t x^{\prime }\left (t \right )+a y^{\prime }\left (t \right )-x \left (t \right )=0 \\ x^{\prime }\left (t \right ) y^{\prime }\left (t \right )+t y^{\prime }\left (t \right )-y \left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x \left (t \right )=t x^{\prime }\left (t \right )+f \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \\ y \left (t \right )=t y^{\prime }\left (t \right )+g \left (x^{\prime }\left (t \right ), y^{\prime }\left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right )-z \left (t \right ) \\ y^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ z^{\prime }\left (t \right )=x \left (t \right )^{2}+z \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} a x^{\prime }\left (t \right )=\left (b -c \right ) y \left (t \right ) z \left (t \right ) \\ b y^{\prime }\left (t \right )=\left (c -a \right ) z \left (t \right ) x \left (t \right ) \\ c z^{\prime }\left (t \right )=\left (a -b \right ) x \left (t \right ) y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )=x \left (t \right ) y \left (t \right ) \\ y^{\prime }\left (t \right )+z^{\prime }\left (t \right )=y \left (t \right ) z \left (t \right ) \\ x^{\prime }\left (t \right )+z^{\prime }\left (t \right )=x \left (t \right ) z \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right ) \left (y \left (t \right )^{2}-z \left (t \right )^{2}\right ) \\ y^{\prime }\left (t \right )=-y \left (t \right ) \left (z \left (t \right )^{2}+x \left (t \right )^{2}\right ) \\ z^{\prime }\left (t \right )=z \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} \left (x \left (t \right )-y \left (t \right )\right ) \left (x \left (t \right )-z \left (t \right )\right ) x^{\prime }\left (t \right )=f \left (t \right ) \\ \left (-x \left (t \right )+y \left (t \right )\right ) \left (y \left (t \right )-z \left (t \right )\right ) y^{\prime }\left (t \right )=f \left (t \right ) \\ \left (-x \left (t \right )+z \left (t \right )\right ) \left (-y \left (t \right )+z \left (t \right )\right ) z^{\prime }\left (t \right )=f \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }\left (x \right )=2 y_{1} \left (x \right )+1-6 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x} \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} y_{1}^{\prime }\left (x \right )=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x \\ y_{2}^{\prime }\left (x \right )=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} t x^{\prime }\left (t \right )+2 x \left (t \right )=15 y \left (t \right ) \\ t y^{\prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2} \\ y^{\prime }\left (t \right )={\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=-2 t x_{1} \left (t \right )^{2} \\ x_{2}^{\prime }\left (t \right )=\frac {x_{2} \left (t \right )+t}{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )={\mathrm e}^{t -x_{1} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=2 \,{\mathrm e}^{x_{1} \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=y \left (t \right ) \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )^{2}}{x \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x_{1}^{\prime }\left (t \right )=\frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )} \\ x_{2}^{\prime }\left (t \right )=x_{2} \left (t \right )-x_{1} \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {{\mathrm e}^{-x \left (t \right )}}{t} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right ) {\mathrm e}^{-y \left (t \right )}}{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t -y \left (t \right )}{-x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )-t}{-x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=y \left (t \right ) \\ y^{\prime \prime }\left (t \right )=x \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )=0 \\ x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right )=0 \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=3 x \left (t \right )+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime \prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right ) \\ y^{\prime }\left (t \right )=-2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
unknown |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=x \left (t \right )^{2}+y \left (t \right )^{2} \\ y^{\prime }\left (t \right )=2 x \left (t \right ) y \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-\frac {1}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {x \left (t \right )}{y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\frac {y \left (t \right )}{x \left (t \right )-y \left (t \right )} \\ y^{\prime }\left (t \right )=\frac {x \left (t \right )}{x \left (t \right )-y \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=\sin \left (x \left (t \right )\right ) \cos \left (y \left (t \right )\right ) \\ y^{\prime }\left (t \right )=\cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }\left (t \right )=\frac {1}{y \left (t \right )} \\ {\mathrm e}^{t} y^{\prime }\left (t \right )=\frac {1}{x \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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\[ {}\left [\begin {array}{c} x^{\prime }\left (t \right )=-4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }\left (t \right )=6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
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