| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=0 \end {array} \] |
✓ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a \end {array} \] |
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| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \end {array} \] |
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| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1 \end {array} \] |
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| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x \end {array} \] |
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| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x y \end {array} \] |
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| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +y \end {array} \] |
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| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +b y \end {array} \] |
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| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \end {array} \] |
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| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=b y \end {array} \] |
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| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a x +b y^{2} \end {array} \] |
✓ |
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| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=0 \end {array} \] |
✓ |
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| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a \end {array} \] |
✓ |
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✓ |
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| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x \end {array} \] |
✓ |
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| 15 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +y \end {array} \] |
✓ |
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| 16 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +b y \end {array} \] |
✓ |
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| 17 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=y \end {array} \] |
✓ |
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| 18 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=b y \end {array} \] |
✓ |
✓ |
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| 19 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=a x +b y^{2} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 20 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r} \end {array} \] | ✓ | ✓ | ✓ | ✗ |
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| 21 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r x} \end {array} \] |
✓ |
✓ |
✓ |
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| 22 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{r \,x^{2}} \end {array} \] |
✓ |
✓ |
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| 23 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }&=\frac {a x +b y^{2}}{y} \end {array} \] |
✓ |
✓ |
✓ |
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| 24 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \sin \left (x \right ) y x y^{\prime }&=0 \end {array} \] |
✓ |
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| 25 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi& =0 \end {array} \] |
✓ |
✓ |
✓ |
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| 26 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right )+y \end {array} \] |
✓ |
✓ |
✓ |
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| 27 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right )+y^{2} \end {array} \] |
✓ |
✓ |
✓ |
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| 28 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )+\frac {y}{x} \end {array} \] |
✓ |
✓ |
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| 29 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \end {array} \] |
✗ |
✗ |
✗ |
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| 30 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +y+b y^{2} \end {array} \] |
✓ |
✓ |
✓ |
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| 31 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=0 \end {array} \] |
✓ |
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| 32 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime }&=0 \end {array} \] |
✓ |
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| 33 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e} y^{\prime }&=0 \end {array} \] |
✓ |
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| 34 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \pi y^{\prime }&=0 \end {array} \] |
✓ |
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| 35 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 36 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 37 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=1 \end {array} \] |
✓ |
✓ |
✓ |
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| 38 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }&=\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
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| 39 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -1\right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 40 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 41 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 42 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \sin \left (x \right ) y^{\prime }&=0 \end {array} \] | ✓ | ✓ | ✓ | ✓ |
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| 43 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \pi y \sin \left (x \right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 44 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sin \left (x \right ) y^{\prime }&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 45 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \sin \left (x \right ) {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 46 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}&=0 \end {array} \] |
✓ |
✓ |
✓ |
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| 47 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{n}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 48 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{n}&=0 \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 49 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=x \end {array} \] |
✓ |
✓ |
✓ |
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| 50 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=x +y \end {array} \] |
✓ |
✓ |
✓ |
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| 51 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y}{x} \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 52 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y^{2}}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 53 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {y^{3}}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 54 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}&=\frac {y^{2}}{x} \end {array} \] |
✓ |
✓ |
✓ |
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| 55 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{y x} \end {array} \] |
✓ |
✓ |
✓ |
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| 56 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x y^{3}} \end {array} \] |
✓ |
✓ |
✓ |
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| 57 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \end {array} \] |
✓ |
✓ |
✓ |
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| 58 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=\frac {1}{x y^{3}} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 59 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \end {array} \] |
✓ |
✓ |
✓ |
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| 60 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1+6 x +y} \end {array} \] |
✓ |
✓ |
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| 61 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{3}} \end {array} \] |
✓ |
✓ |
✓ |
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| 62 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (1+6 x +y\right )^{{1}/{4}} \end {array} \] |
✓ |
✓ |
✓ |
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| 63 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (a +b x +y\right )^{4} \end {array} \] |
✓ |
✓ |
✓ |
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| 64 | \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \end {array} \] | ✓ | ✓ | ✗ | ✗ |
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| 65 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left (a +b x +c y\right )^{6} \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 66 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \] |
✓ |
✓ |
✓ |
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| 67 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10+{\mathrm e}^{x +y} \end {array} \] |
✓ |
✓ |
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| 68 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \end {array} \] |
✓ |
✓ |
✓ |
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| 69 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
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| 70 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=t +y \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=t +y \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \] |
✓ |
✓ |
✓ |
✓ |
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| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )&=y \left (t \right )+t +\sin \left (t \right )+\cos \left (t \right )\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}\\ \end {array} \] |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y t&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
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| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (x_{0} \right )&=y_{0}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=0\\ y \left (1\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=\sin \left (t \right )\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
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| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime }+y&=t\\ y \left (1\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y+y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a t +1\right ) y^{\prime }+y&=t\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
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| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (-3\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
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| 2 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
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| 3 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=0\\ y \left (0\right )&=1\\ \end {array} \]
Series expansion around \(x=0\). |
✗ |
✗ |
✗ |
✗ |
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| 4 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 5 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=1 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 6 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=2 x^{4}+x^{3}+x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 8 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\frac {1}{x^{3}} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 9 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+2 y x&=\sqrt {x} \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 10 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x}&=0 \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 11 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✗ |
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| 12 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✗ |
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| 13 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\tan \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
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| 14 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime }+y&=\cos \left (x \right )+\sin \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|