| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
1+y-y^{\prime } t&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
16.930 |
|
| \begin{align*}
1+2 y-2 y^{\prime } t&=\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| \begin{align*}
y&=-y^{\prime } t +\frac {{y^{\prime }}^{5}}{5} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| \begin{align*}
y&=t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.051 |
|
| \begin{align*}
y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
y&=t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.679 |
|
| \begin{align*}
t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
46.856 |
|
| \begin{align*}
y^{\prime }&=\frac {-t^{2}+y^{2}}{t y} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.996 |
|
| \begin{align*}
y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.779 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.671 |
|
| \begin{align*}
\cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.735 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.578 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.458 |
|
| \begin{align*}
-\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.013 |
|
| \begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.087 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.456 |
|
| \begin{align*}
3 y+y^{\prime }&=-10 \sin \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.762 |
|
| \begin{align*}
3 t +\left (t -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.971 |
|
| \begin{align*}
y-t +\left (y+t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.812 |
|
| \begin{align*}
y-x +y^{\prime }&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
148.625 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.316 |
|
| \begin{align*}
x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
56.277 |
|
| \begin{align*}
t^{2}-y+\left (-t +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.449 |
|
| \begin{align*}
t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.563 |
|
| \begin{align*}
\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.991 |
|
| \begin{align*}
t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
7.010 |
|
| \begin{align*}
y+y^{\prime }&=5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.141 |
|
| \begin{align*}
t y+y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.460 |
|
| \begin{align*}
x^{\prime }+\frac {x}{y}&=y^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.449 |
|
| \begin{align*}
t r^{\prime }+r&=t \cos \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.784 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.655 |
|
| \begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.554 |
|
| \begin{align*}
y&=y^{\prime } t +3 {y^{\prime }}^{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
4.862 |
|
| \begin{align*}
y-y^{\prime } t&=2 y^{2} \ln \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.749 |
|
| \begin{align*}
y-y^{\prime } t&=-2 {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.689 |
|
| \begin{align*}
y-y^{\prime } t&=-4 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
2 x -y-2+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.069 |
|
| \begin{align*}
\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.625 |
|
| \begin{align*}
{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.242 |
|
| \begin{align*}
\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
13.651 |
|
| \begin{align*}
y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }&=0 \\
y \left (0\right ) &= \pi \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.056 |
|
| \begin{align*}
\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.199 |
|
| \begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
707.825 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✓ |
18.441 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
46.386 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
50.898 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{-2+t} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.701 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.240 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.863 |
|
| \begin{align*}
2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.920 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.419 |
|
| \begin{align*}
3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.635 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= -22 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
7.907 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.563 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.615 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.466 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+18 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.029 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.542 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.185 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime }+49 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+6 y^{\prime } t +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
a y^{\prime \prime }+b y^{\prime }+c y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
28.785 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+a t y^{\prime }+b y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
18.866 |
|
| \begin{align*}
4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
t y^{\prime \prime }+2 y^{\prime }+16 t y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.765 |
|
| \begin{align*}
y^{\prime \prime }+b y^{\prime }+c y&=0 \\
y \left (\pi \right ) &= 0 \\
y \left (2 \pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.954 |
|
| \begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.519 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.259 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.236 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.436 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.777 |
|
| \begin{align*}
8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.502 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.398 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.649 |
|
| \begin{align*}
y^{\prime \prime }+8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime \prime }+7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.840 |
|
| \begin{align*}
4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
8.459 |
|
| \begin{align*}
7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.207 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.309 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
3 y^{\prime \prime }-y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.985 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.969 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \begin{align*}
y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.262 |
|