|
ID |
problem |
ODE |
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1(a) |
\(y y^{\prime } = x\) |
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1(b) |
\(y^{\prime }-y = x^{3}\) |
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1(c) |
\(y^{\prime }+y \cot \left (x \right ) = x\) |
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1(d) |
\(y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )\) |
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1(e) |
\(y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right )\) |
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1(f) |
\(y^{\prime }+y \ln \left (x \right ) = x^{-x}\) |
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2(a) |
\(x y^{\prime }+y = x\) |
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2(b) |
\(-y+x y^{\prime } = x^{3}\) |
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2(c) |
\(x y^{\prime }+n y = x^{n}\) |
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2(d) |
\(x y^{\prime }-n y = x^{n}\) |
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2(e) |
\(\left (x^{3}+x \right ) y^{\prime }+y = x\) |
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3(a) |
\(\cot \left (x \right ) y^{\prime }+y = x\) |
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3(b) |
\(\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )\) |
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3(c) |
\(\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right )\) |
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3(a) |
\(\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right )\) |
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4(a) |
\(y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )\) |
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4(b) |
\(y^{\prime } \cos \left (x \right )+y = \sin \left (2 x \right )\) |
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4(c) |
\(y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right )\) |
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4(d) |
\(\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )\) |
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5(a) |
\(\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x\) |
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5(b) |
\(\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1}\) |
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5(c) |
\(\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0\) |
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5(d) |
\(\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}\) |
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