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# |
ODE |
CAS classification |
Solved? |
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\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2}
\] |
[_separable] |
✓ |
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\[
{}x {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
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\[
{}\left (x +1\right ) {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
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\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
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\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}3 x^{4} {y^{\prime }}^{2}-x y-y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}y = x {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
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\[
{}{y^{\prime }}^{3} = \frac {y^{2}}{x}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {1}{x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {1}{y^{3} x^{2}}
\] |
[_separable] |
✓ |
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\[
{}{y^{\prime }}^{4} = \frac {1}{x y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
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\[
{}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}}
\] |
[_separable] |
✓ |
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\[
{}x {y^{\prime }}^{2}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
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\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
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\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}{y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}y = \left (x +1\right ) {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
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\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
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\[
{}{y^{\prime }}^{2}-9 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
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\[
{}{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
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\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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