| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
{y^{\prime \prime }}^{n}&=0 \\
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| 4 |
\begin{align*}
a y^{\prime \prime }&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
a {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
a {y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
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| 8 |
\begin{align*}
{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
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| 9 |
\begin{align*}
y^{\prime \prime }&=x \\
\end{align*} |
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| 10 |
\begin{align*}
{y^{\prime \prime }}^{2}&=x \\
\end{align*} |
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| 11 |
\begin{align*}
{y^{\prime \prime }}^{3}&=0 \\
\end{align*} |
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| 12 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
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| 13 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
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| 14 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 15 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
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| 16 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} |
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| 17 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
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| 18 | \begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
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| 19 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x \\
\end{align*} |
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| 20 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
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| 21 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
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| 22 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }+y&=0 \\
\end{align*} |
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| 23 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
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| 24 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1 \\
\end{align*} |
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| 25 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x \\
\end{align*} |
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| 26 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=1+x \\
\end{align*} |
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| 27 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+x +1 \\
\end{align*} |
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| 28 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
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| 29 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
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| 30 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
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| 31 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
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| 32 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x \\
\end{align*} |
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| 33 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1+x \\
\end{align*} |
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| 34 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+x +1 \\
\end{align*} |
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| 35 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{3}+x^{2}+x +1 \\
\end{align*} |
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| 36 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
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| 37 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\cos \left (x \right ) \\
\end{align*} |
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| 38 | \begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 39 |
\begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
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| 40 |
\begin{align*}
y^{\prime \prime }+y&=1+x \\
\end{align*} |
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| 41 |
\begin{align*}
y^{\prime \prime }+y&=x^{2}+x +1 \\
\end{align*} |
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| 42 |
\begin{align*}
y^{\prime \prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
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| 43 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
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| 44 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
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| 45 |
\begin{align*}
y {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
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| 46 |
\begin{align*}
y {y^{\prime \prime }}^{2}+{y^{\prime }}^{3}&=0 \\
\end{align*} |
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| 47 |
\begin{align*}
y^{2} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
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| 48 |
\begin{align*}
y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 49 |
\begin{align*}
y^{3} {y^{\prime \prime }}^{2}+y^{\prime } y&=0 \\
\end{align*} |
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| 50 |
\begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
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| 51 |
\begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\
\end{align*} |
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| 52 |
\begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
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| 2 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y^{2} {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime \prime }+\left (\sin \left (x \right )+2 x \right ) y^{\prime }+\cos \left (y\right ) y {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime } y^{\prime \prime }+y^{2}&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime } y^{\prime \prime }+y^{n}&=0 \\
\end{align*} |
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| 8 |
\begin{align*}
y^{\prime }&=\left (x +y\right )^{4} \\
\end{align*} |
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| 9 |
\begin{align*}
y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (y^{2}+3\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 10 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 11 |
\begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 12 |
\begin{align*}
3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
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| 13 |
\begin{align*}
10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y}&=0 \\
\end{align*} |
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| 14 |
\begin{align*}
10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \\
\end{align*} |
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| 15 |
\begin{align*}
y^{\prime \prime }-\frac {2 y}{x^{2}}&=x \,{\mathrm e}^{-\sqrt {x}} \\
\end{align*} |
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| 16 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=x \\
\end{align*} |
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| 17 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
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| 18 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y&=0 \\
\end{align*} |
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| 19 | \begin{align*}
x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
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| 20 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \\
\end{align*} |
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| 21 |
\begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \\
\end{align*} |
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| 22 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y&=4 \cos \left (\ln \left (1+x \right )\right ) \\
\end{align*} |
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| 23 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
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| 24 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\
\end{align*} |
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| 25 |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=x^{5} \\
\end{align*} |
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| 25 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\
\end{align*} |
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| 26 |
\begin{align*}
y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\
\end{align*} |
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| 27 |
\begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x^{m +1} \\
\end{align*} |
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| 28 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\
\end{align*} |
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| 29 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
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| 30 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right ) \\
\end{align*} |
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| 31 |
\begin{align*}
y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \\
\end{align*} |
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| 32 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\
\end{align*} |
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| 33 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x^{2}} \sec \left (x \right ) \\
\end{align*} |
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| 34 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 \left (x^{2}+1\right ) y&=0 \\
\end{align*} |
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| 35 |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y&=0 \\
\end{align*} |
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| 36 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
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| 37 | \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 38 |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*} |
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| 39 |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 \cos \left (x \right ) \\
\end{align*} |
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| 40 |
\begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 41 |
\begin{align*}
y^{\prime }&=x -y^{2} \\
\end{align*} |
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| 42 |
\begin{align*}
-2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
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| 43 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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| 44 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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| 45 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-5\right ) y&=0 \\
\end{align*} |
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| 46 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
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| 47 |
\begin{align*}
y^{\prime \prime \prime }-y x&=0 \\
\end{align*} |
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| 48 |
\begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
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| 49 |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right ) \\
y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \\
\end{align*} |
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