| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8401 |
\begin{align*}
y^{\prime }-\tan \left (y x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
1.080 |
|
| 8402 |
\begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8403 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8404 |
\begin{align*}
y^{\prime \prime }+4 y&=t^{2}+3 \,{\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8405 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8406 |
\begin{align*}
x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8407 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| 8408 |
\begin{align*}
-\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.081 |
|
| 8409 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime }-y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
1.081 |
|
| 8410 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+6 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 8411 |
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.081 |
|
| 8412 |
\begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 8413 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-4 x_{1}+2 x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-2 x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 8414 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.081 |
|
| 8415 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 8416 |
\begin{align*}
2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 y^{\prime } x -2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 8417 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 8418 |
\begin{align*}
x^{\prime }&=2 x-y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=y-2 z-3 x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 8419 |
\begin{align*}
x^{\prime }&=6 x-3 y \\
y^{\prime }&=2 x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.082 |
|
| 8420 |
\begin{align*}
y^{\prime } x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 8421 |
\begin{align*}
\left (2+x \right ) y^{\prime }-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| 8422 |
\begin{align*}
1+2 y-2 y^{\prime } t&=\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.083 |
|
| 8423 |
\begin{align*}
y^{\prime }+y&=2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 8424 |
\begin{align*}
y+x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 8425 |
\begin{align*}
4 y+y^{\prime \prime }&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 8426 |
\begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.084 |
|
| 8427 |
\begin{align*}
x&=t x^{\prime }-{x^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 8428 |
\begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| 8429 |
\begin{align*}
x^{\prime \prime }&=\frac {1}{\left (1+t \right )^{3}} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8430 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+x_{3} \\
x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\
x_{3}^{\prime }&=-9 x_{1}+4 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 ) &= 17 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8431 |
\begin{align*}
y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8432 |
\begin{align*}
y^{\prime }-y^{\prime \prime } x +{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8433 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=x^{3}+x^{2}+x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8434 |
\begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8435 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8436 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-3 x_{2}-2 x_{3} \\
x_{2}^{\prime }&=8 x_{1}-5 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=-4 x_{1}+3 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.085 |
|
| 8437 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sec \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 8438 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 8439 |
\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
1.086 |
|
| 8440 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 8441 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| 8442 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 8443 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }&=t^{2}-{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 8444 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 8445 |
\begin{align*}
y^{\prime \prime }-4 y&=8 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 8446 |
\begin{align*}
4 y+y^{\prime \prime }&=x^{2}+3 x \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| 8447 |
\begin{align*}
-\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 8448 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 8449 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.088 |
|
| 8450 |
\begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 8451 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 8452 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=6 y+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| 8453 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=50 \cos \left (x \right ) \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8454 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8455 |
\begin{align*}
\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8456 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8457 |
\begin{align*}
y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 5 \\
y^{\prime \prime \prime }\left (0\right ) &= 19 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8458 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.089 |
|
| 8459 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 8460 |
\begin{align*}
\left (1+a \right ) x y^{\prime }+x^{2} y^{\prime \prime }&=x^{k} f \left (x^{k} y, k y+y^{\prime } x \right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.090 |
|
| 8461 |
\begin{align*}
x^{\prime }&=-4 x+y \\
y^{\prime }&=2 x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 8462 |
\begin{align*}
y^{\prime \prime }+9 y&=36 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.090 |
|
| 8463 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 8464 |
\begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 8465 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=3 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| 8466 |
\begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (2 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8467 |
\begin{align*}
x_{1}^{\prime }&=2 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8468 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8469 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8470 |
\begin{align*}
y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8471 |
\begin{align*}
y^{\prime }&=2 \cos \left (x \right ) \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8472 |
\begin{align*}
y^{\prime \prime }+16 y&=\csc \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8473 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8474 |
\begin{align*}
{x^{\prime }}^{2}&=-4 x+4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| 8475 |
\begin{align*}
{y^{\prime }}^{3} x -y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.093 |
|
| 8476 |
\begin{align*}
y^{\prime \prime }+9 y&=-3 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 8477 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 8478 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (2\right ) &= 10 \\
y^{\prime }\left (2\right ) &= 15 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 8479 |
\begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 8480 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 8481 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 8482 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 8483 |
\begin{align*}
3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| 8484 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=16 x_{1}-5 x_{2} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 8485 |
\begin{align*}
x^{\prime }&=-2 x+3 y \\
y^{\prime }&=-2 x+5 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 8486 |
\begin{align*}
y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| 8487 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 8488 |
\begin{align*}
\left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 8489 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 8490 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=-3 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 8491 |
\begin{align*}
x^{\prime }+x+2 y&=2 \,{\mathrm e}^{-t} \\
y^{\prime }+y+z&=1 \\
z^{\prime }+z&=1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 8492 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (w t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 8493 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\
x_{2}^{\prime }&=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 8494 |
\begin{align*}
x^{\prime }&=2 x+2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 8495 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.099 |
|
| 8496 |
\begin{align*}
\left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.099 |
|
| 8497 |
\begin{align*}
4 x^{\prime \prime }-20 x^{\prime }+21 x&=0 \\
x \left (0\right ) &= -4 \\
x^{\prime }\left (0\right ) &= -12 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 8498 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 8499 |
\begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 8500 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -16 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.099 |
|