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ID |
problem |
ODE |
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2 |
\(x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0\) |
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3 |
\(y^{\prime }+c y = a\) |
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4 |
\(y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y = 0\) |
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5 |
\(\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right ) = 0\) |
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6 |
\(y^{\prime } = \frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x}\) |
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16 (a) |
\(v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}\) |
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16 (b) |
\(v^{\prime }+u^{2} v = \sin \left (u \right )\) |
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17 (a) |
\(\sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}\) |
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18 |
\(v^{\prime }+\frac {2 v}{u} = 3\) |
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ID |
problem |
ODE |
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4 (a) |
\(\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0\) |
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4 (b) |
\(y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0\) |
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4 (c) |
\(y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )\) |
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5 |
\(x^{\prime } = k \left (A -n x\right ) \left (M -m x\right )\) |
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6 |
\(y^{\prime } = 1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )}\) |
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|
ID |
problem |
ODE |
|
1 |
\(y^{2} = x \left (y-x \right ) y^{\prime }\) |
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2 |
\(2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0\) |
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3 |
\(2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g\) |
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4 |
\(\sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right ) = 0\) |
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5 |
\(x +y y^{\prime } = m y\) |
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6 |
\(\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0\) |
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|
8 |
\(\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime } = \frac {T}{t \sqrt {t^{2}-T^{2}}}-t\) |
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|
ID |
problem |
ODE |
|
1 |
\(y^{\prime }+y x = x\) |
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|
2 |
\(y^{\prime }+\frac {y}{x} = \sin \left (x \right )\) |
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3 |
\(y^{\prime }+\frac {y}{x} = \frac {\sin \left (x \right )}{y^{3}}\) |
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4 |
\(p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )}\) |
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5 |
\(\left (T \ln \left (t \right )-1\right ) T = t T^{\prime }\) |
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6 |
\(y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}\) |
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7 |
\(y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )\) |
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|
ID |
problem |
ODE |
|
2 |
\(x {y^{\prime }}^{2}-y+2 y^{\prime } = 0\) |
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|
3 |
\(2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0\) |
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4 |
\(y^{\prime } = {\mathrm e}^{z -y^{\prime }}\) |
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5 |
\(\sqrt {t^{2}+T} = T^{\prime }\) |
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7 |
\(\left (x^{2}-1\right ) {y^{\prime }}^{2} = 1\) |
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8 |
\(y^{\prime } = \left (x +y\right )^{2}\) |
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|
ID |
problem |
ODE |
|
1 |
\(\theta ^{\prime \prime } = -p^{2} \theta \) |
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2 (eq 39) |
\(\sec \left (\theta \right )^{2} = \frac {m s^{\prime }}{k}\) |
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3 (eq 41) |
\(y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}\) |
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4 (eq 50) |
\(\phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}\) |
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8 (eq 68) |
\(y^{\prime } = x \left (a y^{2}+b \right )\) |
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8 (eq 69) |
\(n^{\prime } = \left (n^{2}+1\right ) x\) |
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9 (a) |
\(v^{\prime }+\frac {2 v}{u} = 3 v\) |
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9 (b) |
\(\sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}}\) |
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9 (c) |
\(\sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2}\) |
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9 (d) |
\(\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}}\) |
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9 (e) |
\(y^{\prime } = 1+\frac {2 y}{x -y}\) |
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10 (a) |
\(v^{\prime }+2 v u = 2 u\) |
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10 (b) |
\(1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0\) |
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10 (c) |
\(u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1\) |
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ID |
problem |
ODE |
|
1 (eq 100) |
\(\theta ^{\prime \prime }-p^{2} \theta = 0\) |
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2 |
\(y^{\prime \prime }+y = 0\) |
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3 |
\(y^{\prime \prime }+12 y = 7 y^{\prime }\) |
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4 |
\(r^{\prime \prime }-a^{2} r = 0\) |
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5 |
\(y^{\prime \prime \prime \prime }-a^{4} y = 0\) |
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6 |
\(v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u}\) |
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7 |
\(y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right )\) |
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8 |
\(y^{\prime \prime }+3 y = \sin \left (x \right )+\frac {\sin \left (3 x \right )}{3}\) |
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10 |
\(5 x^{\prime }+x = \sin \left (3 t \right )\) |
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11 |
\(x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime } = {\mathrm e}^{-3 t}\) |
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14 |
\(x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6}\) |
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15 |
\(t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right )\) |
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ID |
problem |
ODE |
|
1 |
\(y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0\) |
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2 |
\(y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = {\mathrm e}^{2 x}\) |
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|
3 |
\(y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )\) |
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8 |
\(x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}\) |
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