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ODE |
Mathematica |
Maple |
Sympy |
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\[
{} \left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0
\]
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\[
{} \left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\]
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\[
{} \left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\]
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\[
{} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\]
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\[
{} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\]
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\[
{} \left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\]
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\[
{} \left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0
\]
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\[
{} a x y {y^{\prime }}^{2}-\left (y^{2} a +b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2} = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} a +b x +c = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0
\]
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\[
{} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+a \,x^{2}+\left (a -1\right ) b = 0
\]
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\[
{} \left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0
\]
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\[
{} \left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\]
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\[
{} \left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0
\]
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\[
{} \left (y^{2}+\left (1-a \right ) x^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} = 0
\]
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\[
{} \left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0
\]
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\[
{} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\]
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\[
{} \left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0
\]
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\[
{} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0
\]
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\[
{} \left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }+y^{2} a -b \,x^{2}-a b = 0
\]
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\[
{} \left (y^{2} a +b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2} = 0
\]
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\[
{} \left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2} = 0
\]
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\[
{} \left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y = 0
\]
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\[
{} x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\]
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\[
{} x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0
\]
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\[
{} \left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right ) = 0
\]
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\[
{} \left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2} = 0
\]
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\[
{} 9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0
\]
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\[
{} x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0
\]
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\[
{} \left (a^{2} \sqrt {x^{2}+y^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {x^{2}+y^{2}}-y^{2} = 0
\]
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\[
{} \left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0
\]
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\[
{} {y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d = 0
\]
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\[
{} f \left (x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) f \left (\frac {x}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) f \left (\frac {y}{\sqrt {x^{2}+y^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}-f \left (x \right ) \left (y^{2} a +b y+c \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}+x y^{\prime }-y = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y = 0
\]
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\[
{} {y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}-a x y y^{\prime }+2 y^{2} a = 0
\]
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\[
{} {y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3} = 0
\]
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\[
{} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\]
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\[
{} {y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x = 0
\]
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\[
{} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\]
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\[
{} {y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\]
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\[
{} {y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6} = 0
\]
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\[
{} a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d = 0
\]
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\[
{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\]
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\[
{} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y-x = 0
\]
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\[
{} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\]
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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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\[
{} x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y = 0
\]
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\[
{} 2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right ) = 0
\]
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\[
{} 2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 x y^{\prime }-x = 0
\]
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\[
{} y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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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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\[
{} x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5} = 0
\]
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\[
{} {y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x = 0
\]
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\[
{} {y^{\prime }}^{4}-4 y \left (x y^{\prime }-2 y\right )^{2} = 0
\]
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\[
{} {y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3} = 0
\]
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\[
{} x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0
\]
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\[
{} {y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}} = 0
\]
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\[
{} {y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1} = 0
\]
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\[
{} {y^{\prime }}^{n}-f \left (x \right ) g \left (y\right ) = 0
\]
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\[
{} a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y = 0
\]
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\[
{} x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y = 0
\]
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\[
{} \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\]
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\[
{} \sqrt {1+{y^{\prime }}^{2}}+x {y^{\prime }}^{2}+y = 0
\]
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\[
{} x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0
\]
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\[
{} a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\]
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\[
{} y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x = 0
\]
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\[
{} a y \sqrt {1+{y^{\prime }}^{2}}-2 x y y^{\prime }+y^{2}-x^{2} = 0
\]
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\[
{} f \left (x^{2}+y^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\]
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\[
{} a \left ({y^{\prime }}^{3}+1\right )^{{1}/{3}}+b x y^{\prime }-y = 0
\]
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\[
{} \ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0
\]
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\[
{} \ln \left (y^{\prime }\right )+a \left (x y^{\prime }-y\right ) = 0
\]
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\[
{} y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\]
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\[
{} \sin \left (y^{\prime }\right )+y^{\prime }-x = 0
\]
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\[
{} a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0
\]
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\[
{} {y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y = 0
\]
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\[
{} \left (1+{y^{\prime }}^{2}\right ) \sin \left (x y^{\prime }-y\right )^{2}-1 = 0
\]
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\[
{} \left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0
\]
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\[
{} a \,x^{n} f \left (y^{\prime }\right )+x y^{\prime }-y = 0
\]
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\[
{} f \left (x {y^{\prime }}^{2}\right )+2 x y^{\prime }-y = 0
\]
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\[
{} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y = 0
\]
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\[
{} y^{\prime } = F \left (\frac {y}{x +a}\right )
\]
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\[
{} y^{\prime } = 2 x +F \left (y-x^{2}\right )
\]
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\[
{} y^{\prime } = -\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right )
\]
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\[
{} y^{\prime } = F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x}
\]
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