| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (2 x +1\right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
|
✓ |
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| \[
{} y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} -\left (1+x \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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| \[
{} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✗ |
✓ |
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| \[
{} y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} a^{2} y+2 x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -y+x \left (2 x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -2 y-x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} a \left (a +1\right ) y-2 x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} -\left (m^{2}-n \left (n +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} -\left (k^{2}-p \left (p +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
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| \[
{} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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✗ |
✗ |
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| \[
{} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0
\]
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✗ |
✓ |
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| \[
{} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} -2 \left (1-x \right ) y+2 \left (3-x \right ) x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x \left (1+x \right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = k^{2} y
\]
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✓ |
✓ |
✗ |
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| \[
{} B y+\left (a -x \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 2 \left (3 x +1\right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (2-x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
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| \[
{} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y+\left (b x +a \right )^{4} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} -y+x y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{3} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+\left (\operatorname {b0} \,x^{4}+\operatorname {a0} \right ) y^{\prime }+x \left (a^{2}-x^{2}\right ) \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0
\]
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✗ |
✗ |
✗ |
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| \[
{} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (8 x^{4}+10 x^{2}+1\right ) y-4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime } = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} -\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime } = a y
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (-x^{2} a +2\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} -x^{2} y^{\prime }+x^{3} y^{\prime \prime } = -x^{2}+3
\]
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✓ |
✓ |
✓ |
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| \[
{} \left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime } = f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right )
\]
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✓ |
✓ |
✓ |
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| \[
{} f \left (x \right )^{2} y^{\prime \prime } = 3 f \left (x \right )^{3}-a f \left (x \right )^{5}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+2 y^{\prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+2 y^{\prime }-y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-2 k y^{\prime }-2 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-y^{\prime }+y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-4 y^{\prime }+20 y = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 4
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
\]
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✓ |
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }+y^{\prime }+y = x^{2}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
\]
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✓ |
✓ |
✓ |
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| \[
{} y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime }+y^{\prime } = x^{2}+2 x
\]
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✓ |
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✓ |
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| \[
{} y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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✓ |
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| \[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (x \right )^{2}
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\]
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|