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ODE |
Mathematica |
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\[
{} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2} = 0
\]
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\[
{} \left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\]
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\[
{} \left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2}
\]
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\[
{} \left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\]
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\[
{} \left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0
\]
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\[
{} \left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0
\]
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\[
{} \left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0
\]
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\[
{} \left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\]
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\[
{} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\]
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\[
{} \left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0
\]
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\[
{} 2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0
\]
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\[
{} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\]
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\[
{} 4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0
\]
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\[
{} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\]
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\[
{} 9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0
\]
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\[
{} \left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\]
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\[
{} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\]
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\[
{} \left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+y^{2} a = 0
\]
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\[
{} a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0
\]
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\[
{} 4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\]
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\[
{} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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\[
{} 3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0
\]
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\[
{} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0
\]
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\[
{} 9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0
\]
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\[
{} {y^{\prime }}^{3} = b x +a
\]
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\[
{} {y^{\prime }}^{3} = a \,x^{n}
\]
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\[
{} {y^{\prime }}^{3}+x -y = 0
\]
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\[
{} {y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right )
\]
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\[
{} {y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2}
\]
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\[
{} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{\prime }+a -b x = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\]
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\[
{} {y^{\prime }}^{3}-7 y^{\prime }+6 = 0
\]
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\[
{} {y^{\prime }}^{3}-x y^{\prime }+a y = 0
\]
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\[
{} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}+a x y^{\prime }-a y = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0
\]
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\[
{} {y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-a x y y^{\prime }+2 y^{2} a = 0
\]
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\[
{} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\]
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\[
{} {y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0
\]
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\[
{} {y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0
\]
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\[
{} {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\]
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\[
{} {y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0
\]
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\[
{} {y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\]
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\[
{} {y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+x y \left (y^{2}+x y+x^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\]
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\[
{} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\]
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\[
{} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\]
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\[
{} 3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\]
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\[
{} 4 {y^{\prime }}^{3}+4 y^{\prime } = x
\]
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\[
{} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\]
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\[
{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\]
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\[
{} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\]
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\[
{} x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\]
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\[
{} 2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0
\]
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\[
{} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0
\]
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\[
{} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\]
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\[
{} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\]
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\[
{} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\]
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\[
{} x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\]
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\[
{} 2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0
\]
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\[
{} x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1
\]
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\[
{} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\]
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\[
{} y {y^{\prime }}^{3}-3 x y^{\prime }+3 y = 0
\]
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\[
{} 2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y = 0
\]
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\[
{} \left (x +2 y\right ) {y^{\prime }}^{3}+3 {y^{\prime }}^{2} \left (x +y\right )+\left (y+2 x \right ) y^{\prime } = 0
\]
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\[
{} y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\]
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\[
{} y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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\[
{} 4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\]
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\[
{} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\]
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\[
{} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\]
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\[
{} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\]
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\[
{} {y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2}
\]
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\[
{} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0
\]
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\[
{} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\]
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\[
{} {y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0
\]
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\[
{} {y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0
\]
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\[
{} 2 {y^{\prime }}^{4}-y y^{\prime }-2 = 0
\]
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\[
{} {y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3} = 0
\]
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\[
{} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\]
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