| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10401 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=\sec \left (2 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10402 |
\begin{align*}
x^{\prime }+3 x-y&=0 \\
y^{\prime }+y-3 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10403 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10404 |
\begin{align*}
y^{\prime }&=y^{2}-y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| 10405 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=5 x_{1}-3 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10406 |
\begin{align*}
t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10407 |
\begin{align*}
4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10408 |
\begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10409 |
\begin{align*}
y^{\prime \prime }+y \cos \left (x \right )&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10410 |
\begin{align*}
a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.544 |
|
| 10411 |
\begin{align*}
y^{\prime \prime }+y&=\frac {2}{\sin \left (x \right )^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10412 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| 10413 |
\begin{align*}
x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 90 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10414 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2}+x_{3} \\
x_{2}^{\prime }&=6 x_{1}-x_{2} \\
x_{3}^{\prime }&=-x_{1}-2 x_{2}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10415 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10416 |
\begin{align*}
a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.545 |
|
| 10417 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10418 | \begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.545 |
|
| 10419 |
\begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10420 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10421 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| 10422 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\sin \left (3 x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10423 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10424 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=14 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10425 |
\begin{align*}
8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10426 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10427 |
\begin{align*}
x^{\prime }&=-2 x+y+z \\
y^{\prime }&=-3 x+2 y+3 z \\
z^{\prime }&=x-y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10428 |
\begin{align*}
y^{\prime }&=\frac {2 \sqrt {y-1}}{3} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10429 |
\begin{align*}
y^{\prime \prime }+6 y&=\cos \left (x \right )^{2} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10430 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}-x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10431 |
\begin{align*}
x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.546 |
|
| 10432 |
\begin{align*}
y+\left (1-x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.546 |
|
| 10433 |
\begin{align*}
\left (x +y^{2}\right ) y^{\prime \prime }&=2 \left (x -y^{2}\right ) {y^{\prime }}^{3}-y^{\prime } \left (1+4 y^{\prime } y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.546 |
|
| 10434 |
\begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10435 |
\begin{align*}
y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10436 |
\begin{align*}
x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\
y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10437 | \begin{align*}
x^{\prime }&=-4 x+2 y \\
y^{\prime }&=3 x-2 y \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.546 |
|
| 10438 |
\begin{align*}
y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10439 |
\begin{align*}
y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10440 |
\begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10441 |
\begin{align*}
x^{\prime }-y&=t \\
x+y^{\prime }&=t^{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10442 |
\begin{align*}
y^{\prime \prime }-3 y&=x \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10443 |
\begin{align*}
y^{\prime \prime }+k y&={\mathrm e}^{i \omega t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| 10444 |
\begin{align*}
x_{1}^{\prime }&=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}-\frac {5 x_{3}}{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 3 \\
x_{3} \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10445 |
\begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
0.547 |
|
| 10446 |
\begin{align*}
x_{1}^{\prime }&=9 x_{1}-2 x_{2}+9 t \\
x_{2}^{\prime }&=5 x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10447 |
\begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=\left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10448 |
\begin{align*}
4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.547 |
|
| 10449 |
\begin{align*}
y^{\prime \prime }&=a \left (-y+y^{\prime } x \right )^{k} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.547 |
|
| 10450 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10451 |
\begin{align*}
y^{\prime }&=\frac {1}{y-3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10452 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10453 |
\begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10454 |
\begin{align*}
x^{\prime \prime }-s x&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.547 |
|
| 10455 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10456 | \begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=5 \sqrt {x} \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✗ | 0.547 |
|
| 10457 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| 10458 |
\begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.548 |
|
| 10459 |
\begin{align*}
x^{\prime \prime }+x&=3 t^{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10460 |
\begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=3 x-8 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10461 |
\begin{align*}
x^{3} y^{\prime }-x^{3}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10462 |
\begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10463 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10464 |
\begin{align*}
y^{\prime \prime }+2 p y^{\prime }+\omega _{n}^{2} y&=\omega _{n}^{2} t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| 10465 |
\begin{align*}
y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10466 |
\begin{align*}
\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=4\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10467 |
\begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10468 |
\begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -3 y x&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10469 |
\begin{align*}
\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10470 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-4 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10471 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10472 |
\begin{align*}
x^{\prime }&=6 x-y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10473 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| 10474 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10475 | \begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y-x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.549 |
|
| 10476 |
\begin{align*}
9 y+6 y^{\prime }+y^{\prime \prime }&=27 \,{\mathrm e}^{-6 x} \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10477 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+5 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10478 |
\begin{align*}
y^{\prime }&=\ln \left (y-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10479 |
\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.549 |
|
| 10480 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10481 |
\begin{align*}
x^{2} y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10482 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| 10483 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\
x_{2}^{\prime }&=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10484 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-t^{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10485 |
\begin{align*}
b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| 10486 |
\begin{align*}
y^{\prime \prime }+4 y&=2 \cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10487 |
\begin{align*}
x -x^{2}-y^{2}+y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10488 |
\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}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10489 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=\left (t +2\right ) \sin \left (\pi t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10490 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| 10491 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10492 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+1 \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10493 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10494 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10495 | \begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.550 |
|
| 10496 |
\begin{align*}
x^{\prime }&=3 x+t \\
y^{\prime }&=-y+2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10497 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10498 |
\begin{align*}
q^{\prime \prime }+q&=t \sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| 10499 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=-3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|
| 10500 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.551 |
|