|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.332 |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }-\left (\nu \left (\nu +1\right ) \left (x^{2}-1\right )+n^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.059 |
|
|
\[
{}\left (-x^{2}+1\right )^{2} y^{\prime \prime }-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (\nu \left (\nu +1\right ) \left (-x^{2}+1\right )-\mu ^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.054 |
|
|
\[
{}a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.394 |
|
|
\[
{}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.486 |
|
|
\[
{}\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.263 |
|
|
\[
{}\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.838 |
|
|
\[
{}\left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.900 |
|
|
\[
{}\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }-c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.636 |
|
|
\[
{}\left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.691 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+A y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.497 |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.009 |
|
|
\[
{}\left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+\left (\left (x^{2}+1\right ) \left (a^{2} x^{2}-\lambda \right )+m^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.033 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (a \,x^{2}+b x +c \right ) y^{\prime }+m y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.437 |
|
|
\[
{}x^{6} y^{\prime \prime }-x^{5} y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.619 |
|
|
\[
{}x^{6} y^{\prime \prime }+\left (3 x^{2}+a \right ) x^{3} y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.237 |
|
|
\[
{}x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.320 |
|
|
\[
{}x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.150 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.177 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.206 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (2 x^{n -1}+a \,x^{2}+b x \right ) y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.123 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.833 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+a^{2} b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
3.280 |
|
|
\[
{}x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.824 |
|
|
\[
{}\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.375 |
|
|
\[
{}\left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
3.908 |
|
|
\[
{}x \left (x^{n}+1\right ) y^{\prime \prime }+\left (\left (a -b \right ) x^{n}+a -n \right ) y^{\prime }+b \left (-a +1\right ) x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.449 |
|
|
\[
{}x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.439 |
|
|
\[
{}x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.664 |
|
|
\[
{}x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
11.459 |
|
|
\[
{}\left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.484 |
|
|
\[
{}\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.280 |
|
|
\[
{}\left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{m +1}+a n -a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.805 |
|
|
\[
{}\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.977 |
|
|
\[
{}x^{2} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (n +1\right ) x \left (a^{2} x^{2 n}-b^{2}\right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.341 |
|
|
\[
{}\left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-b n +\beta \right ) x^{n -2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
5.145 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.354 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.323 |
|
|
\[
{}2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.447 |
|
|
\[
{}\left (a \,x^{n}+b \right )^{m +1} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.369 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.745 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.769 |
|
|
\[
{}y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.321 |
|
|
\[
{}y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.381 |
|
|
\[
{}y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.315 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.437 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.430 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.399 |
|
|
\[
{}y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.552 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.641 |
|
|
\[
{}y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.598 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.753 |
|
|
\[
{}y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.490 |
|
|
\[
{}y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.615 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.560 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+c \left (a \,{\mathrm e}^{\lambda x}+b -c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.585 |
|
|
\[
{}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.491 |
|
|
\[
{}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.770 |
|
|
\[
{}y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.497 |
|
|
\[
{}y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.541 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.789 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.735 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.648 |
|
|
\[
{}y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}-\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.543 |
|
|
\[
{}y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.609 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.536 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.927 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{\mu x}\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.097 |
|
|
\[
{}y^{\prime \prime }+\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{\mu x}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.632 |
|
|
\[
{}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.558 |
|
|
\[
{}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
114.465 |
|
|
\[
{}\frac {1}{\sqrt {y^{2}+x^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {y^{2}+x^{2}}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
8.092 |
|
|
\[
{}y+x +x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.870 |
|
|
\[
{}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.728 |
|
|
\[
{}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
8.059 |
|
|
\[
{}\left (x +1\right ) y^{2}-x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.385 |
|
|
\[
{}2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
23.681 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.499 |
|
|
\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.182 |
|
|
\[
{}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
29.338 |
|
|
\[
{}y^{2}-x y+x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.840 |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
101.037 |
|
|
\[
{}y^{3}+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.668 |
|
|
\[
{}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.915 |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.878 |
|
|
\[
{}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.846 |
|
|
\[
{}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.550 |
|
|
\[
{}y+2 x y^{2}-y^{3} x^{2}+2 x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.689 |
|
|
\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.266 |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.674 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right )
\] |
[_linear] |
✓ |
1.661 |
|
|
\[
{}x y^{\prime }+\left (x +1\right ) y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.276 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
1.387 |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2
\] |
[_linear] |
✓ |
1.216 |
|
|
\[
{}x^{2} y^{\prime }+\left (-2 x +1\right ) y = x^{2}
\] |
[_linear] |
✓ |
1.581 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y = y^{{5}/{2}}
\] |
[_rational, _Bernoulli] |
✓ |
1.945 |
|