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ID |
problem |
ODE |
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1 (i) |
\(x^{\prime } = 3 t^{2}+4 t\) |
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1 (ii) |
\(x^{\prime } = b \,{\mathrm e}^{t}\) |
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1 (iii) |
\(x^{\prime } = \frac {1}{t^{2}+1}\) |
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1 (iv) |
\(x^{\prime } = \frac {1}{\sqrt {t^{2}+1}}\) |
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1 (v) |
\(x^{\prime } = \cos \left (t \right )\) |
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1 (vi) |
\(x^{\prime } = \frac {\cos \left (t \right )}{\sin \left (t \right )}\) |
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2 (i) |
\(x^{\prime } = x^{2}-3 x+2\) |
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2 (ii) |
\(x^{\prime } = b \,{\mathrm e}^{x}\) |
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2 (iii) |
\(x^{\prime } = \left (x-1\right )^{2}\) |
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2 (iv) |
\(x^{\prime } = \sqrt {x^{2}-1}\) |
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2 (v) |
\(x^{\prime } = 2 \sqrt {x}\) |
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2 (vi) |
\(x^{\prime } = \tan \left (x\right )\) |
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3 (i) |
\(3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime } = 0\) |
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3 (ii) |
\(1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0\) |
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3 (iii) |
\(x^{\prime } = \cos \left (\frac {x}{t}\right )\) |
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3 (iv) |
\(\left (t^{2}-x^{2}\right ) x^{\prime } = t x\) |
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3 (v) |
\({\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t} = 2 t\) |
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3 (vi) |
\(2 t +3 x+\left (3 t -x\right ) x^{\prime } = t^{2}\) |
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4 (i) |
\(x^{\prime }+2 x = {\mathrm e}^{t}\) |
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4 (ii) |
\(x^{\prime }+x \tan \left (t \right ) = 0\) |
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4 (iii) |
\(x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right )\) |
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4 (iv) |
\(t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3}\) |
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4 (v) |
\(x^{\prime }+2 t x+t x^{4} = 0\) |
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4 (vi) |
\(t x^{\prime }+x \ln \left (t \right ) = t^{2}\) |
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5 |
\(t x^{\prime }+x g \left (t \right ) = h \left (t \right )\) |
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6 |
\(t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0\) |
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ID |
problem |
ODE |
|
1 |
\(x^{\prime } = -\lambda x\) |
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2 |
\([x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]\) |
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3 |
\(t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0\) |
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5 (i) |
\(x^{\prime \prime }-5 x^{\prime }+6 x = 0\) |
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5 (ii) |
\(x^{\prime \prime }-4 x^{\prime }+4 x = 0\) |
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5 (iiI=i) |
\(x^{\prime \prime }-4 x^{\prime }+5 x = 0\) |
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5 (iv) |
\(x^{\prime \prime }+3 x^{\prime } = 0\) |
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6 (i) |
\(x^{\prime \prime }-3 x^{\prime }+2 x = 0\) |
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6 (ii) |
\(x^{\prime \prime }+x = 0\) |
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6 (iii) |
\(x^{\prime \prime }+2 x^{\prime }+x = 0\) |
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6 (iv) |
\(x^{\prime \prime }-2 x^{\prime }+2 x = 0\) |
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ID |
problem |
ODE |
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7 (i) |
\(x^{\prime \prime }-x = t^{2}\) |
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7 (ii) |
\(x^{\prime \prime }-x = {\mathrm e}^{t}\) |
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7 (iii) |
\(x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right )\) |
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7 (iv) |
\(x^{\prime \prime }-x^{\prime }+x = \sin \left (2 t \right )\) |
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7 (v) |
\(x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right )\) |
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7 (vi) |
\(x^{\prime \prime }+x = \cos \left (t \right )\) |
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