| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
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| 1(b) |
\begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
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| 1(c) |
\begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
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| 1(d) |
\begin{align*}
y^{\prime }&=k y \\
\end{align*} |
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| 1(e) |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
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| 1(f) |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
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| 1(h) |
\begin{align*}
x y^{\prime }+y&=y^{\prime } \sqrt {1-x^{2} y^{2}} \\
\end{align*} |
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| 1(i) |
\begin{align*}
x y^{\prime }&=y+x^{2}+y^{2} \\
\end{align*} |
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| 1(j) |
\begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
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| 1(k) |
\begin{align*}
2 x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
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| 1(L) |
\begin{align*}
x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
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| 1(m) |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
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| 1(n) |
\begin{align*}
\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime }&=y \\
\end{align*} |
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| 1(o) |
\begin{align*}
1+y^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
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| 2(a) |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x}-x \\
\end{align*} |
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| 2(b) |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
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| 2(c) |
\begin{align*}
\left (x +1\right ) y^{\prime }&=x \\
\end{align*} |
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| 2(d) | \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 2(e) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\arctan \left (x \right ) \\
\end{align*} |
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| 2(f) |
\begin{align*}
x y^{\prime }&=1 \\
\end{align*} |
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| 2(g) |
\begin{align*}
y^{\prime }&=\arcsin \left (x \right ) \\
\end{align*} |
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| 2(h) |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
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| 2(i) |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x \\
\end{align*} |
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| 2(j) |
\begin{align*}
\left (x^{2}-3 x +2\right ) y^{\prime }&=x \\
\end{align*} |
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| 3(a) |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
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| 3(b) |
\begin{align*}
y^{\prime }&=2 \sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| 3(c) |
\begin{align*}
y^{\prime }&=\ln \left (x \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
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| 3(d) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=1 \\
y \left (2\right ) &= 0 \\
\end{align*} |
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| 3(e) |
\begin{align*}
x \left (x^{2}-4\right ) y^{\prime }&=1 \\
y \left (1\right ) &= 0 \\
\end{align*} |
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| 3(f) |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
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| 4 |
\begin{align*}
y^{\prime }&=1+2 y x \\
\end{align*} |
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| 5 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
y^{\prime }&=\frac {2 x y^{2}}{1-x^{2} y} \\
\end{align*} |
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| 7 |
\begin{align*}
2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
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| 1(b) |
\begin{align*}
y^{\prime }&=4 y x \\
\end{align*} |
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| 1(c) |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
\end{align*} |
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| 1(d) |
\begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
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| 1(e) |
\begin{align*}
\ln \left (y\right ) y-x y^{\prime }&=0 \\
\end{align*} |
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| 1(f) |
\begin{align*}
x y^{\prime }&=\left (-4 x^{2}+1\right ) \tan \left (y\right ) \\
\end{align*} |
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| 1(g) |
\begin{align*}
y^{\prime } \sin \left (y\right )&=x^{2} \\
\end{align*} |
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| 1(h) |
\begin{align*}
y^{\prime }-y \tan \left (x \right )&=0 \\
\end{align*} |
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| 1(i) |
\begin{align*}
x y y^{\prime }&=-1+y \\
\end{align*} |
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| 1(j) |
\begin{align*}
x y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
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| 2(a) |
\begin{align*}
y y^{\prime }&=x +1 \\
y \left (1\right ) &= 3 \\
\end{align*} |
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| 2(b) |
\begin{align*}
x^{2} y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
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| 2(c) |
\begin{align*}
\frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
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| 2(d) |
\begin{align*}
y^{2} y^{\prime }&=x +2 \\
y \left (0\right ) &= 4 \\
\end{align*} |
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| 2(e) |
\begin{align*}
y^{\prime }&=x^{2} y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
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| 2(e) |
\begin{align*}
\left (y+1\right ) y^{\prime }&=-x^{2}+1 \\
y \left (-1\right ) &= -2 \\
\end{align*} |
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| 3 |
\begin{align*}
\frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \\
\end{align*} |
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| 4 | \begin{align*}
y^{\prime } y^{\prime \prime }&=x \left (x +1\right ) \\
y \left (1\right ) &= 3 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime }-y x&=0 \\
\end{align*} |
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| 1(b) |
\begin{align*}
y^{\prime }+y x&=x \\
\end{align*} |
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| 1(c) |
\begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
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| 1(d) |
\begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
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| 1(e) |
\begin{align*}
2 y-x^{3}&=x y^{\prime } \\
\end{align*} |
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| 1(f) |
\begin{align*}
y^{\prime }+2 y x&=0 \\
\end{align*} |
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| 1(g) |
\begin{align*}
x y^{\prime }-3 y&=x^{4} \\
\end{align*} |
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| 1(h) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
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| 1(i) |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=2 x \csc \left (x \right ) \\
\end{align*} |
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| 1(j) |
\begin{align*}
y-x +x y \cot \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
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| 2(a) |
\begin{align*}
y^{\prime }-y x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
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| 2(b) |
\begin{align*}
y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| 2(c) |
\begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
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| 2(d) |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
y \left (1\right ) &= 3 \\
\end{align*} |
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| 2(e) |
\begin{align*}
y^{\prime }+4 y&={\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| 2(f) |
\begin{align*}
y x +x^{2} y^{\prime }&=2 x \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| 3(a) |
\begin{align*}
x y^{\prime }+y&=x^{4} y^{3} \\
\end{align*} |
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| 3(b) | \begin{align*}
x y^{2} y^{\prime }+y^{3}&=x \cos \left (x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 3(c) |
\begin{align*}
x y^{\prime }+y&=x y^{2} \\
\end{align*} |
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| 3(d) |
\begin{align*}
y^{\prime }+y x&=x y^{4} \\
\end{align*} |
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| 4(a) |
\begin{align*}
\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=y^{2} \\
\end{align*} |
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| 4(b) |
\begin{align*}
-x y^{\prime }+y&=y^{\prime } y^{2} {\mathrm e}^{y} \\
\end{align*} |
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| 4(c) |
\begin{align*}
x y^{\prime }+2&=x^{3} \left (-1+y\right ) y^{\prime } \\
\end{align*} |
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| 6 |
\begin{align*}
x y^{\prime }&=2 x^{2} y+y \ln \left (x \right ) \\
\end{align*} |
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| 7 |
\begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
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| 2 |
\begin{align*}
\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
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| 3 |
\begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
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| 4 |
\begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
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| 5 |
\begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
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| 6 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
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| 7 |
\begin{align*}
\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime }&={\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \\
\end{align*} |
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| 8 |
\begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
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| 9 |
\begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
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| 10 |
\begin{align*}
2 x y^{3}+\cos \left (x \right ) y+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
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| 11 |
\begin{align*}
\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}&=1 \\
\end{align*} |
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| 12 |
\begin{align*}
2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
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| 13 |
\begin{align*}
\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x&=0 \\
\end{align*} |
✓ |
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| 14 |
\begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
✓ |
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| 15 |
\begin{align*}
x \ln \left (y\right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 16 |
\begin{align*}
{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
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| 17 |
\begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
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| 18 | \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| 19 |
\begin{align*}
3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 20 |
\begin{align*}
\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }&=1 \\
\end{align*} |
✓ |
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| 21 |
\begin{align*}
\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y}&=0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
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| 1(b) |
\begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
✓ |
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| 1(c) |
\begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
✓ |
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| 1(d) |
\begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
✓ |
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| 1(e) |
\begin{align*}
x y^{\prime }&=y+2 x \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
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| 1(f) |
\begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 1(g) |
\begin{align*}
x y^{\prime }&=2 x -6 y \\
\end{align*} |
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| 1(h) |
\begin{align*}
x y^{\prime }&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
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| 1(i) |
\begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
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| 1(j) |
\begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 4(a) |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
✓ |
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| 4(b) |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
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| 4(c) |
\begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
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| 4(d) |
\begin{align*}
y^{\prime }&=\frac {x +y-1}{x +4 y+2} \\
\end{align*} |
✓ |
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| 4(e) |
\begin{align*}
2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(a) |
\begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(b) |
\begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(c) | \begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 7(a) |
\begin{align*}
y^{\prime }&=\sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 7(b) |
\begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7(c) |
\begin{align*}
y^{\prime }&=\frac {x^{2}-y x}{y^{2} \cos \left (\frac {x}{y}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 7(d) |
\begin{align*}
y^{\prime }&=\frac {y \tan \left (\frac {y}{x}\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(b) |
\begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(c) |
\begin{align*}
x y^{\prime }+y+3 x^{3} y^{4} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
y+\left (x -2 x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(g) |
\begin{align*}
x +3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(i) |
\begin{align*}
\ln \left (y\right ) y-2 y x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(j) |
\begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(k) |
\begin{align*}
x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(b) |
\begin{align*}
x y y^{\prime \prime }&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
x^{2} y^{\prime \prime }&=2 x y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(f) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(g) |
\begin{align*}
x y^{\prime \prime }+y^{\prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) |
\begin{align*}
\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
y y^{\prime \prime }&=y^{2} y^{\prime }+{y^{\prime }}^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 2(c) |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
|
| 3(a) |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
x^{2} y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
\sec \left (x \right ) y^{\prime }&=\sec \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{x^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 1(f) |
\begin{align*}
y^{\prime }&=\frac {x +2 y}{2 x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) |
\begin{align*}
x y^{\prime }-y&=2 x \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
x^{2} y^{\prime }-2 y&=3 x^{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
y^{2} y^{\prime }&=x \\
y \left (-1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
\csc \left (x \right ) y^{\prime }&=\csc \left (y\right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
|
| 2(e) |
\begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(f) |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2(g) |
\begin{align*}
2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(h) |
\begin{align*}
\frac {1}{y}-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(a) |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4(b) | \begin{align*}
x y^{\prime \prime }&=y^{\prime }-2 {y^{\prime }}^{3} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 4(c) |
\begin{align*}
y y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4(d) |
\begin{align*}
x y^{\prime \prime }-3 y^{\prime }&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
2 y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(i) |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(j) |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(k) |
\begin{align*}
4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(l) |
\begin{align*}
3 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(m) |
\begin{align*}
y^{\prime \prime }&=4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(n) |
\begin{align*}
4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(o) |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(p) |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(q) |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(r) | \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 2(a) |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (1\right ) &= {\mathrm e}^{2} \\
y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(e) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2+3 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(f) |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(a) |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(b) |
\begin{align*}
2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(c) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(d) |
\begin{align*}
4 x^{2} y^{\prime \prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(e) |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(f) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(g) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(h) |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(i) |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-10 y&=6 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
4 y+y^{\prime \prime }&=3 \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=14 \,{\mathrm e}^{-5 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=25 x^{2}+12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=20 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(i) |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=6 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(j) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(k) |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(a) |
\begin{align*}
y^{\prime \prime }-3 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
4 y+y^{\prime \prime }&=\tan \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=64 x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2(a) |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(e) |
\begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(f) |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(g) |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(a) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=\left (x^{2}-1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 5(b) |
\begin{align*}
\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y&=x \left (x +1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 5(c) | \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| 5(d) |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 5(e) |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6(a) |
\begin{align*}
y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 6(b) |
\begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6(c) |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 7 |
\begin{align*}
y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 8 |
\begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 9 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 10 |
\begin{align*}
a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 11 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 12 |
\begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 13 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 14 |
\begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 15 |
\begin{align*}
y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16(a) |
\begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 16(b) |
\begin{align*}
y^{\prime \prime \prime \prime }&=\sin \left (x \right )+24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 17 | \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 18 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=1 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 19(a) |
\begin{align*}
3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 19(b) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 19(c) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 20 |
\begin{align*}
x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
y^{\prime \prime }-y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-5 y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
y^{\prime \prime }-y^{\prime }+4 y&=x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+4 y&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(e) |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x} \\
y \left (2\right ) &= 0 \\
y^{\prime }\left (2\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(f) |
\begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(g) |
\begin{align*}
y^{\prime \prime }&=\tan \left (x \right ) \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(h) |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }&=\ln \left (x \right ) \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= {\mathrm e}^{-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=2 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) | \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 3(c) |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(d) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(e) |
\begin{align*}
y^{\prime \prime }+9 y&=\sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(f) |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(g) |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {2}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(h) |
\begin{align*}
4 y+y^{\prime \prime }&=\tan \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(a) |
\begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(c) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{2}+2 x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(d) |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {x -1}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
y^{\prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
y^{\prime \prime }&=-3 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) solving using series |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(a) solving directly |
\begin{align*}
y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) solving using series |
\begin{align*}
y^{\prime }+y&=1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) solving directly |
\begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) solving using series |
\begin{align*}
y^{\prime }-y&=2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) solving directly |
\begin{align*}
y^{\prime }-y&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) solving using series |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) solving directly |
\begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) solving using series |
\begin{align*}
y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) solving directly |
\begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) solving using series |
\begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) solving directly |
\begin{align*}
y^{\prime }-y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) solving using series |
\begin{align*}
x y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(a) solving directly |
\begin{align*}
x y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) solving using series |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 2(b) solving directly |
\begin{align*}
x^{2} y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) solving using series |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(c) solving directly | \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
|
| 2(d) solving using series |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime }&=\frac {1}{\sqrt {-x^{2}+1}} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
y^{\prime }&=y+1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 solved using series |
\begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 solved directly |
\begin{align*}
y^{\prime }&=x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y x -y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }+2 x y^{\prime }-y&=x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 1(d) |
\begin{align*}
y^{\prime \prime }+y^{\prime }-x^{2} y&=1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 1(e) |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4(a) |
\begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 8 |
\begin{align*}
y^{\prime \prime }-2 x y^{\prime }+2 y p&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 1(b) |
\begin{align*}
x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 1(d) |
\begin{align*}
\left (1+3 x \right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) |
\begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
x^{2} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
x^{3} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(e) |
\begin{align*}
x^{4} y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 3(a) |
\begin{align*}
x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 3(b) |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(c) |
\begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+4 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(d) |
\begin{align*}
x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 4(a) |
\begin{align*}
4 x y^{\prime \prime }+3 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4(c) |
\begin{align*}
2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4(d) |
\begin{align*}
2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 | \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ |
|
| 6 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| 8 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(c) |
\begin{align*}
x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 4 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✗ |
|
| 5 |
\begin{align*}
3 \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✗ |
|
| 6 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 7 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2(a) |
\begin{align*}
x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(x) |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+2 y x&=x^{2} \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 1(b) |
\begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}-x \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 1(d) |
\begin{align*}
2 y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(a) |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(b) |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(c) |
\begin{align*}
x y^{\prime \prime }-4 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(e) |
\begin{align*}
2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(f) |
\begin{align*}
x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 2(g) |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
|
| 2(h) |
\begin{align*}
x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
|
| 3(b) | \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). | ✗ | ✓ | ✓ | ✗ |
|
| 3(c) |
\begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
|
| 3(d) |
\begin{align*}
x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✓ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✗ |
|
| 1(c) |
\begin{align*}
p \left (1+p \right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
y^{\prime \prime }-y&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 7(a) |
\begin{align*}
L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
|
| 7(b) |
\begin{align*}
L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 7(c) |
\begin{align*}
L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 3(a) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-5 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t} \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 3(c) |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 3(d) |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 4(a) |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+3 y&=2 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 4(c) |
\begin{align*}
y^{\prime \prime }+y^{\prime }+2 y&=t \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| 4(d) |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 3 |
\begin{align*}
i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \\
i \left (0\right ) &= 8 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right ) \\
y^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+3 y \left (t \right ) \\
y^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(c) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+t -1 \\
y^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right )-5 t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
y^{\prime }\left (t \right )&=y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right ) \\
y^{\prime }\left (t \right )&=y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
x^{\prime }\left (t \right )&=-3 x \left (t \right )+4 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(b) |
\begin{align*}
x^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=5 x \left (t \right )+2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(c) |
\begin{align*}
x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(d) |
\begin{align*}
x^{\prime }\left (t \right )&=4 x \left (t \right )-3 y \left (t \right ) \\
y^{\prime }\left (t \right )&=8 x \left (t \right )-6 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(e) |
\begin{align*}
x^{\prime }\left (t \right )&=2 x \left (t \right ) \\
y^{\prime }\left (t \right )&=3 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(f) |
\begin{align*}
x^{\prime }\left (t \right )&=-4 x \left (t \right )-y \left (t \right ) \\
y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(g) |
\begin{align*}
x^{\prime }\left (t \right )&=7 x \left (t \right )+6 y \left (t \right ) \\
y^{\prime }\left (t \right )&=2 x \left (t \right )+6 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1(h) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=4 x \left (t \right )+5 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5(b) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )-5 t +2 \\
y^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )-8 t -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 2(a) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )-4 y \left (t \right ) \\
y^{\prime }\left (t \right )&=4 x \left (t \right )-7 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(b) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
y^{\prime }\left (t \right )&=4 x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(c) |
\begin{align*}
x^{\prime }\left (t \right )&=-3 x \left (t \right )+\sqrt {2}\, y \left (t \right ) \\
y^{\prime }\left (t \right )&=\sqrt {2}\, x \left (t \right )-2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2(d) |
\begin{align*}
x^{\prime }\left (t \right )&=5 x \left (t \right )+3 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-6 x \left (t \right )-4 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(a) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(b) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \\
y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(c) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )-5 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(d) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right ) \\
y^{\prime }\left (t \right )&=-4 x \left (t \right )+y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(e) |
\begin{align*}
x^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ) \\
y^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ) \\
z^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+z \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3(f) |
\begin{align*}
x^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right )-z \left (t \right ) \\
y^{\prime }\left (t \right )&=2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ) \\
z^{\prime }\left (t \right )&=3 x \left (t \right )-y \left (t \right )+z \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 4(a) |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )-4 t +1 \\
y^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right )+3 t +4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(b) |
\begin{align*}
x^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )-t +3 \\
y^{\prime }\left (t \right )&=x \left (t \right )+4 y \left (t \right )+t -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4(c) |
\begin{align*}
x^{\prime }\left (t \right )&=-4 x \left (t \right )+y \left (t \right )-t +3 \\
y^{\prime }\left (t \right )&=-x \left (t \right )-5 y \left (t \right )+t +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right ) y \left (t \right )+1 \\
y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|
| 2 |
\begin{align*}
x^{\prime }\left (t \right )&=1+y \left (t \right ) t \\
y^{\prime }\left (t \right )&=-x \left (t \right ) t +y \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|