| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.296 |
|
| \begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.026 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.846 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.086 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x +y}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
y^{\prime }&=\left (x -y+5\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.124 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.958 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.407 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.967 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.698 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.351 |
|
| \begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.793 |
|
| \begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
x +y-1+\left (y-x -5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.905 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
137.719 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
21.344 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
2.805 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.601 |
|
| \begin{align*}
y^{\prime }&=-4 x-y \\
x^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x y}{2 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.072 |
|
| \begin{align*}
y^{\prime }&=x^{3} \left (-x +y\right )^{2}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.400 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x +y}}{-1+y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.391 |
|
| \begin{align*}
y^{\prime }-4 y&=32 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
\left (x^{2}-\frac {2}{y^{3}}\right ) y^{\prime }+2 y x -3 x^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.303 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{x}&=x^{2}-4 x +3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.193 |
|
| \begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| \begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
3.658 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.957 |
|
| \begin{align*}
x^{2}+y^{2}+3 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \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] |
✗ |
✗ |
✗ |
✗ |
51.046 |
|
| \begin{align*}
x^{\prime }&=1+\cos \left (t -x\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.772 |
|
| \begin{align*}
y^{3}+4 y \,{\mathrm e}^{x}+\left (2 \,{\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.580 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\sin \left (2 x \right ) x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
x^{\prime }-\frac {x}{t -1}&=t^{2}+2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| \begin{align*}
y^{\prime }&=2-\sqrt {2 x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.136 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )+\sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.281 |
|
| \begin{align*}
y^{\prime }&=\left (2 x +y-1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.918 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.864 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
13.163 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
24.506 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.263 |
|
| \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] |
✗ |
✗ |
✓ |
✗ |
59.987 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
16.276 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
52.777 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y-1}{x +y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.425 |
|
| \begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 x^{2} y^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
114.151 |
|
| \begin{align*}
y^{\prime }&=\left (x +y+1\right )^{2}-\left (x +y-1\right )^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \begin{align*}
x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.609 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.488 |
|
| \begin{align*}
t +x+3+x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \cos \left (x \right ) \\
y \left (\pi \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.310 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.122 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
34.668 |
|
| \begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.286 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.260 |
|
| \begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1}-y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
y&=x y^{\prime }+2 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| \begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}-x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.728 |
|
| \begin{align*}
y^{\prime }+a y&=Q \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| \begin{align*}
m y^{\prime \prime }+k y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| \begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=-50 \sin \left (5 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=\cos \left (\omega t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
6 y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
z^{\prime \prime }+z^{\prime }-z&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-11 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
4 w^{\prime \prime }+20 w^{\prime }+25 w&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.408 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|