| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25501 |
\begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
134.207 |
|
| 25502 |
\begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
134.437 |
|
| 25503 |
\begin{align*}
y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}}&=\frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
134.566 |
|
| 25504 |
\begin{align*}
y^{\prime }&=-\frac {2+x}{x \left (x +1\right )^{2}}-\frac {\left (-x^{2}+x +2\right ) y}{x \left (x +1\right )}+\left (x +1\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
134.750 |
|
| 25505 |
\begin{align*}
\left (a \left (x^{2}+y^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +a \left (x^{2}+y^{2}\right )^{{3}/{2}}-y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
134.908 |
|
| 25506 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
135.153 |
|
| 25507 |
\begin{align*}
\left (y^{4}+y^{2} x^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x -y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
135.281 |
|
| 25508 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
135.398 |
|
| 25509 |
\begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
135.833 |
|
| 25510 |
\begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
135.862 |
|
| 25511 |
\begin{align*}
y y^{\prime }-y&=-\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
136.362 |
|
| 25512 |
\begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
136.540 |
|
| 25513 |
\begin{align*}
2 y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x -1+x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
136.802 |
|
| 25514 |
\begin{align*}
\sin \left (y\right )^{3} y^{\prime \prime }&=\cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
137.031 |
|
| 25515 |
\begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }-l y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
137.047 |
|
| 25516 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
137.419 |
|
| 25517 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
137.838 |
|
| 25518 |
\begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
138.339 |
|
| 25519 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
138.899 |
|
| 25520 |
\begin{align*}
r^{\prime \prime }&=-\frac {k}{r^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
139.143 |
|
| 25521 |
\begin{align*}
2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
139.171 |
|
| 25522 |
\begin{align*}
y y^{\prime }-y&=-\frac {2 x}{9}+A +\frac {B}{\sqrt {x}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
140.005 |
|
| 25523 |
\begin{align*}
\left (-k +p \right ) \left (1+k +p \right ) y+\left (1+k \right ) \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
140.238 |
|
| 25524 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
140.263 |
|
| 25525 |
\begin{align*}
y^{\prime }&=4 \left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
141.079 |
|
| 25526 |
\begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
141.253 |
|
| 25527 |
\begin{align*}
y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
141.918 |
|
| 25528 |
\begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
142.580 |
|
| 25529 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
142.587 |
|
| 25530 |
\begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
142.752 |
|
| 25531 |
\begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
144.240 |
|
| 25532 |
\begin{align*}
-\left (x +1\right ) y+x \left (3-5 x \right ) y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
144.258 |
|
| 25533 |
\begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y+2 \left (1-\left (3-2 k \right ) x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
144.792 |
|
| 25534 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (y y^{\prime }+x \right )&=a^{2} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
144.895 |
|
| 25535 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=t^{{5}/{2}} {\mathrm e}^{-2 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
145.310 |
|
| 25536 |
\begin{align*}
\sqrt {\frac {y}{x}}+\cos \left (x \right )+\left (\sqrt {\frac {x}{y}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
145.401 |
|
| 25537 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
146.064 |
|
| 25538 |
\begin{align*}
\left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
146.133 |
|
| 25539 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
146.654 |
|
| 25540 |
\begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
147.148 |
|
| 25541 |
\begin{align*}
\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
147.262 |
|
| 25542 |
\begin{align*}
y^{\prime \prime }&=\frac {2 y^{\prime }}{x \left (x -2\right )}-\frac {y}{x^{2} \left (x -2\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
148.143 |
|
| 25543 |
\begin{align*}
y^{2}+\left (t^{2}+t y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
148.625 |
|
| 25544 |
\begin{align*}
R^{\prime \prime }&=-\frac {k}{R^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
149.448 |
|
| 25545 |
\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*} |
✓ |
✓ |
✓ |
✓ |
149.622 |
|
| 25546 |
\begin{align*}
x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
149.832 |
|
| 25547 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (2 a +1\right ) y^{\prime }-b \left (2 a +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
150.948 |
|
| 25548 |
\begin{align*}
2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
152.138 |
|
| 25549 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (x +1\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
152.183 |
|
| 25550 |
\begin{align*}
x y \left (1-{y^{\prime }}^{2}\right )&=\left (-y^{2}-a^{2}+x^{2}\right ) y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
152.501 |
|
| 25551 |
\begin{align*}
a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
153.122 |
|
| 25552 |
\begin{align*}
a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
153.499 |
|
| 25553 |
\begin{align*}
y^{\prime \prime }&=-\frac {a x y^{\prime }}{x^{2}+1}-\frac {b y}{\left (x^{2}+1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
153.638 |
|
| 25554 |
\begin{align*}
-\left (x +1\right )^{3} y+y^{\prime } x +x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
153.735 |
|
| 25555 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
154.372 |
|
| 25556 |
\begin{align*}
x^{\prime \prime }&=\frac {k^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
154.849 |
|
| 25557 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2}&=\left (y y^{\prime }+x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
154.943 |
|
| 25558 |
\begin{align*}
y y^{\prime }-y&=-\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
155.015 |
|
| 25559 |
\begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
155.437 |
|
| 25560 |
\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*} |
✗ |
✗ |
✗ |
✗ |
155.714 |
|
| 25561 |
\begin{align*}
x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
155.753 |
|
| 25562 |
\begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
155.812 |
|
| 25563 |
\begin{align*}
n \left (a +n \right ) y+\left (c -\left (1+a \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
155.986 |
|
| 25564 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
156.346 |
|
| 25565 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
156.558 |
|
| 25566 |
\begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
157.172 |
|
| 25567 |
\begin{align*}
{\mathrm e}^{-x} y^{\prime }+y^{2}-2 \,{\mathrm e}^{x} y&=1-{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
157.243 |
|
| 25568 |
\begin{align*}
x^{2} \left (x^{2}+a \right ) y^{\prime \prime }+\left (b \,x^{2}+c \right ) x y^{\prime }+d y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
157.656 |
|
| 25569 |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -20 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
157.699 |
|
| 25570 |
\begin{align*}
y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
159.234 |
|
| 25571 |
\begin{align*}
y^{\prime }&=y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
159.361 |
|
| 25572 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
159.931 |
|
| 25573 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
160.027 |
|
| 25574 |
\begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
160.573 |
|
| 25575 |
\begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
160.696 |
|
| 25576 |
\begin{align*}
2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
160.751 |
|
| 25577 |
\begin{align*}
-\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 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
160.933 |
|
| 25578 |
\begin{align*}
y^{\prime \prime }+4 y&=-3 t^{2}+2 t +3 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
161.198 |
|
| 25579 |
\begin{align*}
\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
162.081 |
|
| 25580 |
\begin{align*}
y^{\prime }&=\frac {y}{x -k \sqrt {x^{2}+y^{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
163.286 |
|
| 25581 |
\begin{align*}
\left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (a \,x^{2}+b \right ) y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
164.038 |
|
| 25582 |
\begin{align*}
x^{\prime }&=a x+g y+\beta z \\
y^{\prime }&=g x+b y+\alpha z \\
z^{\prime }&=\beta x+\alpha y+c z \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
165.232 |
|
| 25583 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
165.549 |
|
| 25584 |
\begin{align*}
2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
165.705 |
|
| 25585 |
\begin{align*}
-9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
165.799 |
|
| 25586 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
166.548 |
|
| 25587 |
\begin{align*}
x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
166.705 |
|
| 25588 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
166.796 |
|
| 25589 |
\begin{align*}
\left (-y+y^{\prime } x \right ) \left (y y^{\prime }+x \right )&=h^{2} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
166.862 |
|
| 25590 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=x +1 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
166.879 |
|
| 25591 |
\begin{align*}
x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
166.926 |
|
| 25592 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
167.035 |
|
| 25593 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
167.194 |
|
| 25594 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
168.349 |
|
| 25595 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
168.477 |
|
| 25596 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\beta -\alpha -\left (\alpha +\beta +2\right ) x \right ) y^{\prime }+n \left (n +\alpha +\beta +1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
169.546 |
|
| 25597 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
170.473 |
|
| 25598 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\left (\alpha -\beta +\left (\alpha +\beta -2\right ) x \right ) y^{\prime }+\left (n +1\right ) \left (n +\alpha +\beta \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
170.788 |
|
| 25599 |
\begin{align*}
y-x \left (x +1\right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
170.911 |
|
| 25600 |
\begin{align*}
y y^{\prime }&=\left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
170.944 |
|