| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
60.187 |
|
| \begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.850 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.984 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.313 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.917 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.907 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+5\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.744 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.226 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.918 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.175 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.799 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.336 |
|
| \begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.739 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.658 |
|
| \begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.806 |
|
| \begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.271 |
|
| \begin{align*}
x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.057 |
|
| \begin{align*}
-4 x -y-1+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
226.204 |
|
| \begin{align*}
2 x -y+\left (4 x +y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
46.355 |
|
| \begin{align*}
2 x -y+4+\left (x -2 y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.139 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\cos \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.976 |
|
| \begin{align*}
y^{\prime }&=-4 x-y \\
x^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
34.690 |
|
| \begin{align*}
y^{\prime }&=x^{3} \left (-x +y\right )^{2}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.800 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.645 |
|
| \begin{align*}
y^{\prime }-4 y&=32 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.267 |
|
| \begin{align*}
\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
5.823 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.433 |
|
| \begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.242 |
|
| \begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.388 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.967 |
|
| \begin{align*}
x^{2}+y^{2}+3 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.593 |
|
| \begin{align*}
1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
60.531 |
|
| \begin{align*}
x^{\prime }&=1+\cos \left (t -x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.566 |
|
| \begin{align*}
y^{3}+4 \,{\mathrm e}^{x} y+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.996 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.659 |
|
| \begin{align*}
x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| \begin{align*}
y^{\prime }&=2-\sqrt {2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.912 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y+\sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
y^{\prime }&=\left (2 x +y-1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
14.396 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
81.508 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.233 |
|
| \begin{align*}
y-2 x -1+\left (x +y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
27.092 |
|
| \begin{align*}
2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.681 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
43.417 |
|
| \begin{align*}
\sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✓ |
✗ |
77.372 |
|
| \begin{align*}
y \left (x -y-2\right )+x \left (-x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
36.131 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.851 |
|
| \begin{align*}
3 x -y-5+\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
126.619 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
24.590 |
|
| \begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
225.620 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.107 |
|
| \begin{align*}
x^{3}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.863 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.793 |
|
| \begin{align*}
t +x+3+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.358 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.464 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.346 |
|
| \begin{align*}
2 \cos \left (2 x +y\right )-x^{2}+\left (\cos \left (2 x +y\right )+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.709 |
|
| \begin{align*}
2 x -y+\left (-3+x +y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
79.912 |
|
| \begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.916 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.521 |
|
| \begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1}-y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.872 |
|
| \begin{align*}
y&=y^{\prime } x +2 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.956 |
|
| \begin{align*}
{y^{\prime }}^{3} x -y {y^{\prime }}^{2}+2&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.584 |
|
| \begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.669 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
36.259 |
|
| \begin{align*}
y^{\prime }+a y&=Q \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.508 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.231 |
|
| \begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.098 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
2 y^{\prime \prime }+18 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.417 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.649 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.037 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \begin{align*}
2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
z^{\prime \prime }+z^{\prime }-z&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-11 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
4 w^{\prime \prime }+20 w^{\prime }+25 w&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \begin{align*}
3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.857 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{3}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= 9 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= {\frac {25}{3}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\
z \left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|