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ID |
problem |
ODE |
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1 |
\(y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}\) |
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2 |
\(y^{\prime } = x \left (\cos \left (y\right )+y\right )\) |
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3 |
\(y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}\) |
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4 |
\(y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )\) |
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5 |
\(y^{\prime } = y+1\) |
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6 |
\(y^{\prime } = x +1\) |
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7 |
\(y^{\prime } = x\) |
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8 |
\(y^{\prime } = y\) |
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9 |
\(y^{\prime } = 0\) |
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10 |
\(y^{\prime } = 1+\frac {\sec \left (x \right )}{x}\) |
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11 |
\(y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}\) |
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12 |
\(y^{\prime } = \frac {2 y}{x}\) |
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13 |
\(y^{\prime } = \frac {2 y}{x}\) |
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14 |
\(y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}\) |
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15 |
\(y^{\prime } = \frac {1}{x}\) |
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16 |
\(y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}\) |
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17 |
\(\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y = 0\) |
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18 |
\(y^{\prime } = \sqrt {\frac {y+1}{y^{2}}}\) |
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19 |
\(y^{\prime } = \sqrt {1-x^{2}-y^{2}}\) |
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20 |
\(y^{\prime }+\frac {y}{3} = \frac {\left (-2 x +1\right ) y^{4}}{3}\) |
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21 |
\(y^{\prime } = \sqrt {y}+x\) |
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23 |
\(x^{2} y^{\prime }+y^{2} = x y y^{\prime }\) |
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24 |
\(y = y^{\prime } x +x^{2} {y^{\prime }}^{2}\) |
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25 |
\(\left (x +y\right ) y^{\prime } = 0\) |
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26 |
\(y^{\prime } x = 0\) |
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27 |
\(\frac {y^{\prime }}{x +y} = 0\) |
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28 |
\(\frac {y^{\prime }}{x} = 0\) |
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29 |
\(y^{\prime } = 0\) |
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30 |
\(y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}\) |
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31 |
\(y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}\) |
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32 |
\(2 t +3 x+\left (x+2\right ) x^{\prime } = 0\) |
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33 |
\(y^{\prime } = \frac {1}{1-y}\) |
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34 |
\(p^{\prime } = a p-b p^{2}\) |
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35 |
\(y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0\) |
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36 |
\(x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}\) |
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37 |
\(y^{\prime } x -2 y+b y^{2} = c \,x^{4}\) |
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38 |
\(y^{\prime } x -y+y^{2} = x^{{2}/{3}}\) |
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39 |
\(u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}\) |
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40 |
\(y y^{\prime }-y = x\) |
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41 |
\(y^{\prime \prime }+2 y^{\prime }+y = 0\) |
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41 |
\(5 y^{\prime \prime }+2 y^{\prime }+4 y = 0\) |
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42 |
\(y^{\prime \prime }+y^{\prime }+4 y = 1\) |
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43 |
\(y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )\) |
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44 |
\(y = x {y^{\prime }}^{2}\) |
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45 |
\(y y^{\prime } = 1-x {y^{\prime }}^{3}\) |
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46 |
\(f^{\prime } = \frac {1}{f}\) |
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47 |
\(t y^{\prime \prime }+4 y^{\prime } = t^{2}\) |
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48 |
\(\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0\) |
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49 |
\(t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0\) |
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50 |
\(t y^{\prime \prime }+y^{\prime } = 0\) |
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51 |
\(t^{2} y^{\prime \prime }-2 y^{\prime } = 0\) |
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52 |
\(y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0\) |
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53 |
\(t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0\) |
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54 |
\(y^{\prime \prime } = 0\) |
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55 |
\(y^{\prime \prime } = 1\) |
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56 |
\(y^{\prime \prime } = f \left (t \right )\) |
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57 |
\(y^{\prime \prime } = k\) |
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58 |
\(y^{\prime } = -4 \sin \left (x -y\right )-4\) |
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59 |
\(y^{\prime }+\sin \left (x -y\right ) = 0\) |
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60 |
\(y^{\prime \prime } = 4 \sin \left (x \right )-4\) |
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61 |
\(y y^{\prime \prime } = 0\) |
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62 |
\(y y^{\prime \prime } = 1\) |
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63 |
\(y y^{\prime \prime } = x\) |
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64 |
\(y^{2} y^{\prime \prime } = x\) |
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65 |
\(y^{2} y^{\prime \prime } = 0\) |
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66 |
\(3 y y^{\prime \prime } = \sin \left (x \right )\) |
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67 |
\(3 y y^{\prime \prime }+y = 5\) |
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68 |
\(a y y^{\prime \prime }+b y = c\) |
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69 |
\(a y^{2} y^{\prime \prime }+b y^{2} = c\) |
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70 |
\(a y y^{\prime \prime }+b y = 0\) |
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71 |
\([x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]\) |
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72 |
\([x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )]\) |
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73 |
\([x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right )]\) |
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74 |
\([x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )]\) |
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75 |
\([x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]\) |
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76 |
\([x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )]\) |
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77 |
\(x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x\) |
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78 |
\(\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x\) |
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78 |
\(\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x\) |
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79 |
\(y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}\) |
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80 |
\(y^{\prime } = y^{2}+x^{2}\) |
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81 |
\(y^{\prime } = 2 \sqrt {y}\) |
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82 |
\(z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}\) |
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83 |
\(y^{\prime } = \sqrt {1-y^{2}}\) |
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84 |
\(y^{\prime } = -1+x^{2}+y^{2}\) |
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85 |
\(y^{\prime } = 2 y \left (x \sqrt {y}-1\right )\) |
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86 |
\(y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}\) |
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87 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
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88 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
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88 |
\(y^{\prime \prime }+y^{\prime }+y = 0\) |
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89 |
\(y^{\prime \prime }-y y^{\prime } = 2 x\) |
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90 |
\(y^{\prime }-y^{2}-x -x^{2} = 0\) |
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