|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.307 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.416 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.791 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.484 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+1 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.953 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.399 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.363 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.384 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.486 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y = t \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
68.273 |
|
|
\[ {}t \left (-1+t \right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 y t^{2} = 0 \] |
unknown |
[[_high_order, _with_linear_symmetries]] |
❇ |
N/A |
0.114 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.389 |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.319 |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.185 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.627 |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-3 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
2.604 |
|
|
\[ {}t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.428 |
|
|
\[ {}\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-t y^{\prime }+y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.586 |
|
|
\[ {}t^{2} \left (3+t \right ) y^{\prime \prime \prime }-3 t \left (2+t \right ) y^{\prime \prime }+6 \left (t +1\right ) y^{\prime }-6 y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.665 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.386 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
1.038 |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.421 |
|
|
\[ {}y^{\left (6\right )}+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
4.017 |
|
|
\[ {}y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.168 |
|
|
\[ {}y^{\left (6\right )}-y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.27 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.159 |
|
|
\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.424 |
|
|
\[ {}y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.607 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.656 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.575 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+4 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.679 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.696 |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
higher_order_laplace |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime \prime \prime \prime }-4 y = 0 \] |
higher_order_laplace |
[[_high_order, _missing_x]] |
✓ |
✓ |
1.06 |
|
|
\[ {}y^{\prime \prime }+\omega ^{2} y = \cos \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.008 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{-t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.82 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.557 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.522 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.308 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.123 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.998 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.614 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.308 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.156 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.484 |
|
|
\[ {}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.079 |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right ) \] |
higher_order_laplace |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
6.35 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.746 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.13 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.247 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.436 |
|
|
\[ {}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.079 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.706 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.864 |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.983 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.102 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = \delta \left (-1+t \right ) \] |
higher_order_laplace |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.005 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.325 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.22 |
|
|
\[ {}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.893 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.126 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.774 |
|
|
\[ {}y^{\prime } = 2 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.367 |
|
|
\[ {}x y^{\prime }+y = x^{2} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.024 |
|
|
\[ {}y^{\prime }+2 x y = x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}2 y^{\prime }+x \left (y^{2}-1\right ) = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.173 |
|
|
\[ {}y^{\prime } = x^{2} \left (1+y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime } = -x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.141 |
|
|
\[ {}y^{\prime } = -x \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.446 |
|
|
\[ {}y^{\prime } = x \ln \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.181 |
|
|
\[ {}y^{\prime } = -x \,{\mathrm e}^{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime } = x \sin \left (x^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.98 |
|
|
\[ {}y^{\prime } = \tan \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.562 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.645 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.52 |
|
|
\[ {}y^{\prime } = x \left (1+y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}y^{\prime } = -\frac {y \left (y+1\right )}{x} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.308 |
|
|
\[ {}y^{\prime } = a y^{\frac {a -1}{a}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.303 |
|
|
\[ {}y^{\prime } = {| y|}+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime } = -1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
2.417 |
|
|
\[ {}y^{\prime }+a y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.499 |
|
|
\[ {}y^{\prime }+3 x^{2} y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.029 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.622 |
|
|
\[ {}x y^{\prime }+3 y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.262 |
|
|
\[ {}x^{2} y^{\prime }+y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.134 |
|
|
\[ {}y^{\prime }+\frac {\left (1+x \right ) y}{x} = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.648 |
|
|
\[ {}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.164 |
|
|
\[ {}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.635 |
|
|
\[ {}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.544 |
|
|
\[ {}y^{\prime }+\frac {k y}{x} = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.545 |
|
|
\[ {}y^{\prime }+\tan \left (k x \right ) y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.376 |
|
|
\[ {}y^{\prime }+3 y = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.32 |
|
|
\[ {}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.088 |
|
|
\[ {}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.0 |
|
|
|
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