| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25201 |
\begin{align*}
1+\frac {1}{1+x^{2}+4 y x +y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 y x +y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
57.881 |
|
| 25202 |
\begin{align*}
2 y^{\prime }&=\left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
57.902 |
|
| 25203 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y&=\left (x -1\right ) \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
57.925 |
|
| 25204 |
\begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.067 |
|
| 25205 |
\begin{align*}
y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.076 |
|
| 25206 |
\begin{align*}
y^{\prime }&=\frac {1}{y^{2}+x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
58.167 |
|
| 25207 |
\begin{align*}
R^{\prime \prime }&=-\frac {k}{R^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.187 |
|
| 25208 |
\begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.309 |
|
| 25209 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
58.337 |
|
| 25210 |
\begin{align*}
y^{2} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
58.353 |
|
| 25211 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+\sqrt {x^{2}-4 x +4 y}+x^{2} \sqrt {x^{2}-4 x +4 y}+x^{3} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
58.482 |
|
| 25212 |
\begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.489 |
|
| 25213 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
58.571 |
|
| 25214 |
\begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-2 y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
58.631 |
|
| 25215 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
58.656 |
|
| 25216 |
\begin{align*}
y^{\prime \prime }+\frac {a^{2}}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
58.864 |
|
| 25217 |
\begin{align*}
y^{\prime }&=\left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
58.968 |
|
| 25218 | \begin{align*}
x^{\prime \prime }&=\frac {k^{2}}{x^{2}} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 59.023 |
|
| 25219 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sinh \left (\lambda x \right )-a^{2} f \left (x \right ) \sinh \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
59.145 |
|
| 25220 |
\begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
59.308 |
|
| 25221 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
59.384 |
|
| 25222 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
59.385 |
|
| 25223 |
\begin{align*}
3 y-7 x +7&=\left (3 x -7 y-3\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
59.456 |
|
| 25224 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
59.479 |
|
| 25225 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
59.504 |
|
| 25226 |
\begin{align*}
\frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
59.580 |
|
| 25227 |
\begin{align*}
y^{\prime }&=y^{2}+x^{n -1} a n -a^{2} x^{2 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
59.898 |
|
| 25228 |
\begin{align*}
y^{\prime }&=a +b y-\sqrt {A +B y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
59.905 |
|
| 25229 |
\begin{align*}
y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
59.928 |
|
| 25230 |
\begin{align*}
x^{\prime }&=3 x-4 y+z+t \\
y^{\prime }&=x-3 z+t^{2} \\
z^{\prime }&=6 y-7 z+t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
60.062 |
|
| 25231 |
\begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 t y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.106 |
|
| 25232 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\
x_{2}^{\prime }&=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\
x_{3}^{\prime }&=x_{1}+2 x_{2}-3 x_{3} \\
x_{4}^{\prime }&=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\
x_{5}^{\prime }&=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
60.178 |
|
| 25233 |
\begin{align*}
-\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 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
60.315 |
|
| 25234 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.319 |
|
| 25235 |
\begin{align*}
y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.328 |
|
| 25236 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
60.365 |
|
| 25237 |
\begin{align*}
2 y^{\prime \prime }&=1+12 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
60.472 |
|
| 25238 | \begin{align*}
y^{\prime }&=\frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2} \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 60.584 |
|
| 25239 |
\begin{align*}
\left (a \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
60.650 |
|
| 25240 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
60.670 |
|
| 25241 |
\begin{align*}
y^{3} {y^{\prime \prime }}^{2}+y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.881 |
|
| 25242 |
\begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.890 |
|
| 25243 |
\begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
60.931 |
|
| 25244 |
\begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
60.937 |
|
| 25245 |
\begin{align*}
y^{\prime }&=\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
61.002 |
|
| 25246 |
\begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
61.076 |
|
| 25247 |
\begin{align*}
{y^{\prime }}^{3}-2 y^{\prime } y+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
61.135 |
|
| 25248 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
61.306 |
|
| 25249 |
\begin{align*}
y^{\prime }&=\frac {y \left (1+y\right )}{x \left (-y-1+y x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
61.467 |
|
| 25250 |
\begin{align*}
y^{2} y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
61.667 |
|
| 25251 |
\begin{align*}
y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
61.681 |
|
| 25252 |
\begin{align*}
y^{\prime }&=\frac {\left (\left (x^{2}+1\right )^{{3}/{2}} x^{2}+\left (x^{2}+1\right )^{{3}/{2}}+y^{2} \left (x^{2}+1\right )^{{3}/{2}}+x^{2} y^{3}+y^{3}\right ) x}{\left (x^{2}+1\right )^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
61.725 |
|
| 25253 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
61.748 |
|
| 25254 |
\begin{align*}
144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
61.770 |
|
| 25255 |
\begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
61.787 |
|
| 25256 |
\begin{align*}
48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
61.806 |
|
| 25257 |
\begin{align*}
\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 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
61.904 |
|
| 25258 | \begin{align*}
y y^{\prime \prime }&=-2 y^{2}+2 {y^{\prime }}^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 61.925 |
|
| 25259 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.033 |
|
| 25260 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.044 |
|
| 25261 |
\begin{align*}
x^{\prime }&=\left (2+x\right ) \left (1-x^{4}\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.044 |
|
| 25262 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+a \,x^{1+k} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.165 |
|
| 25263 |
\begin{align*}
y^{\prime } x&=\lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.167 |
|
| 25264 |
\begin{align*}
y^{\prime }&=a +b y+\sqrt {A +B y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.179 |
|
| 25265 |
\begin{align*}
x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.256 |
|
| 25266 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.309 |
|
| 25267 |
\begin{align*}
\left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
62.431 |
|
| 25268 |
\begin{align*}
y^{\prime }&=a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.431 |
|
| 25269 |
\begin{align*}
3 y \cos \left (x \right )+4 x \,{\mathrm e}^{x}+2 x^{3} y+\left (3 \sin \left (x \right )+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.523 |
|
| 25270 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
62.530 |
|
| 25271 |
\begin{align*}
3 x +3 y-2+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.657 |
|
| 25272 |
\begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.662 |
|
| 25273 |
\begin{align*}
-\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.736 |
|
| 25274 |
\begin{align*}
\sin \left (2 x \right )^{n +1} y^{\prime }&=a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.855 |
|
| 25275 |
\begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.865 |
|
| 25276 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \,x^{2}-c \right ) y^{\prime }+\lambda \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.914 |
|
| 25277 |
\begin{align*}
-\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 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.954 |
|
| 25278 | \begin{align*}
y^{\prime } y-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\
\end{align*} | ✗ | ✓ | ✗ | ✗ | 63.031 |
|
| 25279 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.120 |
|
| 25280 |
\begin{align*}
y^{\prime } y-y&=-\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
63.123 |
|
| 25281 |
\begin{align*}
y^{2} {y^{\prime }}^{2}+2 x y^{\prime } y+a y^{2}+b x +c&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.178 |
|
| 25282 |
\begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.197 |
|
| 25283 |
\begin{align*}
{y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.257 |
|
| 25284 |
\begin{align*}
y^{\prime } y-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
63.414 |
|
| 25285 |
\begin{align*}
y^{\prime } y+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}}&=\frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
63.458 |
|
| 25286 |
\begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.523 |
|
| 25287 |
\begin{align*}
-\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 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.582 |
|
| 25288 |
\begin{align*}
y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.766 |
|
| 25289 |
\begin{align*}
\left (b x +a \right ) y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.827 |
|
| 25290 |
\begin{align*}
y^{\prime } y+x&=m y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.859 |
|
| 25291 |
\begin{align*}
x^{2}-2 y^{2}+x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.872 |
|
| 25292 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
64.002 |
|
| 25293 |
\begin{align*}
y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.064 |
|
| 25294 |
\begin{align*}
y^{\prime } y-y&=\frac {k}{\sqrt {A \,x^{2}+B x +c}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
64.101 |
|
| 25295 |
\begin{align*}
y^{\prime } y-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}}&=\frac {a^{2} \left (x -1\right ) \left (2+x \right )}{4 x^{4}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
64.178 |
|
| 25296 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
64.235 |
|
| 25297 |
\begin{align*}
x^{2}-3 y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.297 |
|
| 25298 | \begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-a^{2} f \left (x \right )+a \lambda \sin \left (\lambda x \right )+a^{2} f \left (x \right ) \sin \left (\lambda x \right )^{2} \\
\end{align*} | ✗ | ✗ | ✗ | ✗ | 64.319 |
|
| 25299 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+1 \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
64.401 |
|
| 25300 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
64.591 |
|