|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.906 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right ) \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \cos \left (x \right ) \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.505 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 9 \ln \left (x \right ) \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.307 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 8 x \ln \left (x \right )^{2} \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.878 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right ) \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.737 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )} \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k} \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
9.447 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.285 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.694 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.26 |
|
|
\[ {}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.375 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.418 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.384 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.375 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.425 |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right ) \] |
reduction_of_order |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.385 |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x} \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.377 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4} \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.298 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x} \] |
reduction_of_order |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.332 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right ) \] |
reduction_of_order |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.333 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right ) \] |
reduction_of_order |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.283 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.226 |
|
|
\[ {}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.273 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.435 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.04 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.569 |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.35 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.457 |
|
|
\[ {}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.389 |
|
|
\[ {}y^{\prime \prime }+x y = \sin \left (x \right ) \] |
second_order_airy, second_order_bessel_ode |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.121 |
|
|
\[ {}y^{\prime \prime }+4 y = \ln \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.698 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.412 |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.507 |
|
|
\[ {}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.806 |
|
|
\[ {}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.441 |
|
|
\[ {}y^{\prime }+y = 8 \,{\mathrm e}^{3 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.39 |
|
|
\[ {}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime }+2 y = 4 t \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.377 |
|
|
\[ {}y^{\prime }-y = 6 \cos \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime }-y = 5 \sin \left (2 t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.362 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.313 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 36 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.35 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.391 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.377 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t} \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.413 |
|
|
\[ {}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.425 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.469 |
|
|
\[ {}y^{\prime \prime }-y = 6 \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.551 |
|
|
\[ {}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.747 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.477 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.529 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.438 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime \prime }+4 y = 9 \sin \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime \prime }+y = 6 \cos \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.542 |
|
|
\[ {}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.015 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.282 |
|
|
\[ {}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (-1+t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.896 |
|
|
\[ {}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.749 |
|
|
\[ {}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.399 |
|
|
\[ {}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.909 |
|
|
\[ {}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
13.737 |
|
|
\[ {}y^{\prime \prime }-y = \operatorname {Heaviside}\left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.349 |
|
|
\[ {}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (-1+t \right )-\operatorname {Heaviside}\left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.668 |
|
|
\[ {}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (-1+t \right ) \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.341 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{1-t} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.24 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.093 |
|
|
\[ {}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.273 |
|
|
\[ {}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.247 |
|
|
\[ {}y^{\prime }+y = \delta \left (t -5\right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}y^{\prime }-2 y = \delta \left (t -2\right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.748 |
|
|
\[ {}y^{\prime }+4 y = 3 \delta \left (-1+t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.901 |
|
|
\[ {}y^{\prime \prime }-4 y = \delta \left (t -3\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.839 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.927 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.868 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.152 |
|
|
\[ {}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.599 |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.829 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.188 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.402 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_erf] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }-2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-2 x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.652 |
|
|
|
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