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ODE |
Mathematica |
Maple |
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\[
{}\left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0
\] |
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\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\] |
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\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\] |
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\[
{}x y y^{\prime \prime }+2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y y^{\prime } = 0
\] |
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\[
{}x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
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\[
{}x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y = 0
\] |
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\[
{}2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
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\[
{}x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2} = 0
\] |
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\[
{}x^{2} \left (x +y\right ) y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0
\] |
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\[
{}a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0
\] |
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\[
{}x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2} = 0
\] |
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\[
{}8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0
\] |
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\[
{}\operatorname {f0} \left (x \right ) y y^{\prime \prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f3} \left (x \right ) y^{2} = 0
\] |
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\[
{}y^{2} y^{\prime \prime }-a = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0
\] |
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\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\] |
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\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+\left (1-2 y\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\] |
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\[
{}\left (y^{2}+x \right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\] |
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\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\] |
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\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+y \left (1-y\right ) y^{\prime } f \left (x \right ) = 0
\] |
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\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
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\[
{}2 y \left (y-1\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (y-1\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
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\[
{}-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
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\[
{}3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
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✓ |
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\[
{}\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
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\[
{}a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
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\[
{}a y \left (y-1\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\] |
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\[
{}a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\] |
✓ |
✓ |
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\[
{}x y^{2} y^{\prime \prime }-a = 0
\] |
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\[
{}\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (y^{2} a +b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\] |
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\[
{}x^{3} y^{2} y^{\prime \prime }+\left (x +y\right ) \left (x y^{\prime }-y\right )^{3} = 0
\] |
✓ |
✓ |
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\[
{}y^{3} y^{\prime \prime }-a = 0
\] |
✓ |
✓ |
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\[
{}y \left (1+y^{2}\right ) y^{\prime \prime }+\left (1-3 y^{2}\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\] |
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\[
{}2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
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\[
{}2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\] |
✓ |
✓ |
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\[
{}\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{{3}/{2}} = 0
\] |
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\[
{}2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 x y-2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 x y\right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2} = 0
\] |
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\[
{}\left (y^{2}-1\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\] |
✓ |
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\[
{}\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+y d = 0
\] |
✓ |
✓ |
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\[
{}\sqrt {y}\, y^{\prime \prime }-a = 0
\] |
✓ |
✓ |
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\[
{}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
✗ |
✓ |
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\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\] |
✓ |
✓ |
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\[
{}h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\] |
✓ |
✓ |
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\[
{}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0
\] |
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\[
{}y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime }-x y^{2} = 0
\] |
✗ |
✗ |
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\[
{}\left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}\left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
✗ |
✓ |
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\[
{}a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\] |
✗ |
✓ |
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\[
{}\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2} = 0
\] |
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✗ |
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\[
{}\left (x^{2}+2 y^{\prime } y^{2}\right ) y^{\prime \prime }+2 y {y^{\prime }}^{3}+3 x y^{\prime }+y = 0
\] |
✗ |
✗ |
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\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }+y^{3} = 0
\] |
✓ |
✓ |
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\[
{}\left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\] |
✓ |
✓ |
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\[
{}\left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\] |
✓ |
✓ |
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\[
{}h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }+f = 0
\] |
✗ |
✗ |
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\[
{}{y^{\prime \prime }}^{2}-a y-b = 0
\] |
✓ |
✓ |
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\[
{}a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\] |
✗ |
✓ |
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\[
{}2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\] |
✓ |
✓ |
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\[
{}3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2} = 0
\] |
✗ |
✗ |
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\[
{}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\] |
✗ |
✗ |
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\[
{}\left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\] |
✓ |
✓ |
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\[
{}\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\] |
✓ |
✗ |
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\[
{}\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0
\] |
✓ |
✗ |
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\[
{}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\] |
✗ |
✗ |
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\[
{}y^{\prime \prime }-f \left (y\right ) = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\] |
✓ |
✓ |
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\[
{}y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\] |
✗ |
✗ |
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\[
{}y^{\prime \prime }+a y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-\left (a x +b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-\left (a \,x^{2}+b \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-a \,x^{n} y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\] |
✗ |
✓ |
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\[
{}y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
✗ |
✓ |
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\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
✗ |
✓ |
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\[
{}y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\] |
✓ |
✓ |
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