| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10001 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 10002 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 10003 |
\begin{align*}
{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| 10004 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10005 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10006 |
\begin{align*}
2 y x +2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10007 |
\begin{align*}
x \left (x +1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 10008 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10009 |
\begin{align*}
y^{\prime \prime } x +\left (2 a x \ln \left (x \right )+1\right ) y^{\prime }+\left (a^{2} x \ln \left (x \right )^{2}+a \ln \left (x \right )+a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.757 |
|
| 10010 |
\begin{align*}
x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10011 |
\begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10012 |
\begin{align*}
y^{\prime \prime }-9 y&=54 t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10013 |
\begin{align*}
y^{\prime \prime }+16 y&=2 \cos \left (4 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10014 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10015 |
\begin{align*}
x_{1}^{\prime }&=-k_{1} x_{1} \\
x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\
x_{3}^{\prime }&=k_{2} x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= m_{0} \\
x_{2} \left (0\right ) &= 0 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10016 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10017 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10018 |
\begin{align*}
y^{\prime \prime }+2 z y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10019 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10020 |
\begin{align*}
5 y^{\prime \prime }-6 y^{\prime }+5 y&=13 \,{\mathrm e}^{x} \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| 10021 |
\begin{align*}
1+y^{\prime }&=2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10022 |
\begin{align*}
b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| 10023 |
\begin{align*}
y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10024 |
\begin{align*}
y^{\prime \prime }+y-\sin \left (x n \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10025 |
\begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| 10026 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| 10027 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}-2 \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10028 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10029 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+t \\
x_{2}^{\prime }&=-2 x_{1}+x_{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10030 |
\begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| 10031 |
\begin{align*}
x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| 10032 |
\begin{align*}
\left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| 10033 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10034 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10035 |
\begin{align*}
z^{\prime \prime }-2 z^{\prime }-2 z&=0 \\
z \left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10036 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10037 |
\begin{align*}
1+y^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10038 |
\begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10039 |
\begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=8 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10040 |
\begin{align*}
y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| 10041 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| 10042 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10043 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10044 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x +7 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10045 |
\begin{align*}
y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10046 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+x&=t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10047 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=1 \\
x^{\prime }+y^{\prime }+2 x-y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10048 |
\begin{align*}
x^{\prime }&=2 x-6 y \\
y^{\prime }&=2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10049 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10050 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=5 x-3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10051 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.761 |
|
| 10052 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| 10053 |
\begin{align*}
16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10054 |
\begin{align*}
\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10055 |
\begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 y-3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10056 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| 10057 |
\begin{align*}
4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10058 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10059 |
\begin{align*}
y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10060 |
\begin{align*}
x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 x {y^{\prime }}^{2}+x \left (x +2 y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| 10061 |
\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.763 |
|
| 10062 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10063 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10064 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \sinh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.763 |
|
| 10065 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| 10066 |
\begin{align*}
x^{\prime \prime }&=4 \left (t +3\right )^{2} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10067 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&=\sin \left (x \right )-{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10068 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10069 |
\begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.764 |
|
| 10070 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10071 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| 10072 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10073 |
\begin{align*}
-2 y x -2 \left (-x^{2}+1\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| 10074 |
\begin{align*}
y y^{\prime \prime }&={\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.765 |
|
| 10075 |
\begin{align*}
y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10076 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10077 |
\begin{align*}
y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10078 |
\begin{align*}
U^{\prime \prime }+\frac {2 U^{\prime }}{r}+a U&=0 \\
\end{align*} Series expansion around \(r=0\). |
✓ |
✓ |
✓ |
✗ |
0.765 |
|
| 10079 |
\begin{align*}
y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| 10080 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}-2 x_{3} \\
x_{2}^{\prime }&=x_{1}+6 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{1}+6 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10081 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10082 |
\begin{align*}
x^{\prime }-x-2 y&=0 \\
x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10083 |
\begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10084 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10085 |
\begin{align*}
y^{\prime } t +y&=\sin \left (t \right ) \\
y \left (1\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
0.766 |
|
| 10086 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+16 y&=\frac {{\mathrm e}^{-4 t}}{t^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| 10087 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.766 |
|
| 10088 |
\begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10089 |
\begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10090 |
\begin{align*}
{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10091 |
\begin{align*}
5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10092 |
\begin{align*}
y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10093 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+36 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10094 |
\begin{align*}
\left (x -y\right ) y^{\prime \prime }-\left (1+y^{\prime }\right ) \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.767 |
|
| 10095 |
\begin{align*}
x^{\prime }+y^{\prime }-y&={\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10096 |
\begin{align*}
x^{\prime \prime }+x^{\prime }+2 x&=t \sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10097 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sec \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10098 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| 10099 |
\begin{align*}
6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| 10100 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.768 |
|