| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25901 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y+3 \,{\mathrm e}^{x} x^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.218 |
|
| 25902 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.228 |
|
| 25903 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y^{2}&=y x \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.246 |
|
| 25904 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +\left (x +1\right ) y&={\mathrm e}^{x} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.262 |
|
| 25905 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+\left (x +1\right ) y^{\prime }&=\frac {{\mathrm e}^{x}}{x +1} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.289 |
|
| 25906 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x +y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.329 |
|
| 25907 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-12 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.353 |
|
| 25908 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.356 |
|
| 25909 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.360 |
|
| 25910 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-y&=0 \end {array} \]
|
✓ |
✗ |
✗ |
✗ |
51.455 |
|
| 25911 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.468 |
|
| 25912 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.528 |
|
| 25913 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.530 |
|
| 25914 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
51.540 |
|
| 25915 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.565 |
|
| 25916 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y&=0 \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
51.569 |
|
| 25917 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.633 |
|
| 25918 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \]
|
✓ |
✗ |
✗ |
✗ |
51.635 |
|
| 25919 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+24 y^{\prime \prime }+10 y^{\prime }-25 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
51.638 |
|
| 25920 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.669 |
|
| 25921 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-9 y^{\prime \prime }+8 y^{\prime }-2 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.671 |
|
| 25922 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\left (7\right )}-35 y^{\left (5\right )}-35 y^{\prime \prime \prime \prime }+70 y^{\prime \prime \prime }+154 y^{\prime \prime }+105 y^{\prime }+25 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.771 |
|
| 25923 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.875 |
|
| 25924 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
51.880 |
|
| 25925 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.902 |
|
| 25926 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (6\right )}+18 y^{\prime \prime \prime \prime }+81 y^{\prime \prime }&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.904 |
|
| 25927 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }-4 y^{\prime }-4 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.956 |
|
| 25928 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
51.993 |
|
| 25929 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.116 |
|
| 25930 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
52.140 |
|
| 25931 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=16 x^{2} \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
52.214 |
|
| 25932 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }&=4 x^{2}+x \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.223 |
|
| 25933 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=4 x \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.224 |
|
| 25934 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=x^{3}+2 x^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.288 |
|
| 25935 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x^{3}+2 x^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.307 |
|
| 25936 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=8 x^{2} \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
52.368 |
|
| 25937 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \end {array} \]
|
✓ |
✓ |
✗ |
✓ |
52.386 |
|
| 25938 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.418 |
|
| 25939 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \end {array} \]
|
✗ |
✗ |
✓ |
✗ |
52.442 |
|
| 25940 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.491 |
|
| 25941 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.500 |
|
| 25942 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (2 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.519 |
|
| 25943 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.592 |
|
| 25944 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-y&=6 \sin \left (3 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.621 |
|
| 25945 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.651 |
|
| 25946 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.719 |
|
| 25947 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y&=x +\sin \left (x \right )+\cos \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.738 |
|
| 25948 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=x^{2}+{\mathrm e}^{x} \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
52.745 |
|
| 25949 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (2 x \right )+\sin \left (2 x \right )+2 \,{\mathrm e}^{-x} \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
52.750 |
|
| 25950 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.810 |
|
| 25951 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
52.817 |
|
| 25952 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
52.867 |
|
| 25953 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.884 |
|
| 25954 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{x} \end {array} \]
|
✓ |
✗ |
✓ |
✗ |
52.905 |
|
| 25955 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=-2 \,{\mathrm e}^{x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
52.973 |
|
| 25956 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=16 \,{\mathrm e}^{2 x} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
52.976 |
|
| 25957 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.017 |
|
| 25958 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=\sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.020 |
|
| 25959 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=\cos \left (2 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.029 |
|
| 25960 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.031 |
|
| 25961 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.113 |
|
| 25962 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=8 \sin \left (4 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.133 |
|
| 25963 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x^{5}-2 x^{2}+6 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
53.148 |
|
| 25964 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=x^{2}+2 x -6 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.227 |
|
| 25965 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=3 x^{4} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.266 |
|
| 25966 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.273 |
|
| 25967 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.287 |
|
| 25968 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+y&=x^{3}-2 x^{2}+1 \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
53.288 |
|
| 25969 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }&=1 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.305 |
|
| 25970 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+y&=x \,{\mathrm e}^{-x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.342 |
|
| 25971 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \end {array} \]
|
✓ |
✗ |
✓ |
✓ |
53.364 |
|
| 25972 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=x \sin \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.402 |
|
| 25973 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
53.409 |
|
| 25974 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
53.462 |
|
| 25975 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x}+1 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.475 |
|
| 25976 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=4 x^{3}-2 \,{\mathrm e}^{2 x} \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
53.487 |
|
| 25977 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 y^{\prime }+y^{\prime \prime }&=\left (x -2\right ) {\mathrm e}^{x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.520 |
|
| 25978 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 y^{\prime }+y^{\prime \prime }&=72 x \,{\mathrm e}^{-x} \end {array} \]
|
✓ |
✓ |
✗ |
✓ |
53.543 |
|
| 25979 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.587 |
|
| 25980 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
53.600 |
|
| 25981 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (x \right ) \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
53.600 |
|
| 25982 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
53.622 |
|
| 25983 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\csc \left (x \right ) \sec \left (x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.642 |
|
| 25984 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.648 |
|
| 25985 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&={\mathrm e}^{-x} \sec \left (x \right ) \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
53.670 |
|
| 25986 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.680 |
|
| 25987 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (x \right ) x \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
53.704 |
|
| 25988 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )-x \left (t \right )+2 y \left (t \right )&=0\\ \frac {d}{d t}y \left (t \right )+3 x \left (t \right )-2 y \left (t \right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.741 |
|
| 25989 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )&=0\\ \frac {d}{d t}x \left (t \right )+2 \frac {d}{d t}y \left (t \right )&=4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.780 |
|
| 25990 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }\left (t \right )&=-y \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=4 y \left (t \right )+z \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.836 |
|
| 25991 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}y \left (t \right )&=4 y \left (t \right )-z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=2 y \left (t \right )+z \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.907 |
|
| 25992 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )+2 x \left (t \right )-y \left (t \right )&=-\sin \left (t \right )\\ \frac {d}{d t}x \left (t \right )-3 x \left (t \right )+\frac {d}{d t}y \left (t \right )+2 y \left (t \right )&=4 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.947 |
|
| 25993 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d^{2}}{d t^{2}}y \left (t \right )-y \left (t \right )+5 \frac {d}{d t}y \left (t \right )&=t\\ 2 \frac {d}{d t}y \left (t \right )-\frac {d^{2}}{d t^{2}}x \left (t \right )+4 x \left (t \right )&=2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
53.977 |
|
| 25994 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=3 x \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )\\ z^{\prime }\left (t \right )&=3 y \left (t \right )-2 z \left (t \right )\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
53.995 |
|
| 25995 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{3 t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
54.035 |
|
| 25996 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✗ |
✗ |
✗ |
✗ |
54.053 |
|
| 25997 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
54.067 |
|
| 25998 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=12\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✗ |
✗ |
54.135 |
|
| 25999 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=8 t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
54.140 |
|
| 26000 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=4 t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
54.193 |
|