|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.319 |
|
|
\[ {}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.54 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.386 |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Laguerre] |
✓ |
✓ |
3.592 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.169 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.709 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.222 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.204 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.059 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
9.587 |
|
|
\[ {}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.763 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.917 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.838 |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.729 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.42 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.193 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.56 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _exact, _linear, _homogeneous]] |
❇ |
N/A |
0.941 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.532 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
second_order_bessel_ode |
[_Bessel] |
✓ |
✓ |
2.393 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.445 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.552 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.19 |
|
|
\[ {}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \] |
second_order_bessel_ode |
[_Bessel] |
✓ |
✓ |
3.973 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.443 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.565 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.171 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.941 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.313 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x y = 0 \] |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.085 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x y = 0 \] |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.316 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.46 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.976 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.57 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
kovacic, second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.591 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.303 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.395 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.682 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.8 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.677 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.508 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.016 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.828 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.98 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
1.625 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.398 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.838 |
|
|
\[ {}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
12.342 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.143 |
|
|
\[ {}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
8.286 |
|
|
\[ {}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.122 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime }-y = 1 \] |
first_order_laplace |
[_quadrature] |
✓ |
✓ |
0.418 |
|
|
\[ {}2 y^{\prime }+y = 0 \] |
first_order_laplace |
[_quadrature] |
✓ |
✓ |
0.335 |
|
|
\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime }-y = 2 \cos \left (5 t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.654 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.589 |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t} \] |
higher_order_laplace |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right ) \] |
higher_order_laplace |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.597 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.471 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{-4 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime }-y = 1+t \,{\mathrm e}^{t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.439 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.441 |
|
|
\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.731 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.467 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.286 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.791 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.107 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.503 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.454 |
|
|
\[ {}y^{\prime }+y = t \sin \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.716 |
|
|
\[ {}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.717 |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.723 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.665 |
|
|
\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.712 |
|
|
\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.659 |
|
|
\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.484 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime }-3 y = \delta \left (t -2\right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.638 |
|
|
\[ {}y^{\prime }+y = \delta \left (-1+t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.637 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.537 |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.519 |
|
|
|
||||||
|
|
||||||