| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12901 |
\begin{align*}
x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \\
x \left (0\right ) &= 375 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12902 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=3 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12903 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 12904 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\sqrt {t +1} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12905 |
\begin{align*}
x^{\prime }&=-7 x+y-6 z \\
y^{\prime }&=10 x-4 y+12 z \\
z^{\prime }&=2 x-y+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12906 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12907 |
\begin{align*}
x^{\prime }-x-2 y&={\mathrm e}^{t} \\
-4 x+y^{\prime }-3 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12908 |
\begin{align*}
-2 \left (1-3 x \right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=x^{3} \left (x +1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 12909 |
\begin{align*}
3 {y^{\prime \prime }}^{2}-y^{\prime \prime \prime } y^{\prime }-y^{\prime \prime } {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12910 |
\begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12911 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12912 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12913 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 12914 |
\begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| 12915 |
\begin{align*}
3 x^{\prime }+3 x+2 y&={\mathrm e}^{t} \\
4 x-3 y^{\prime }+3 y&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12916 |
\begin{align*}
x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12917 |
\begin{align*}
x^{\prime }+3 x-2 y&={\mathrm e}^{-t} \\
y^{\prime }-x+4 y&=\sin \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| 12918 | \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.773 |
|
| 12919 |
\begin{align*}
4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 12920 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\
x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 12921 |
\begin{align*}
x^{2} y^{\prime \prime }+y&=3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 12922 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 12923 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| 12924 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| 12925 |
\begin{align*}
2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12926 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12927 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12928 |
\begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12929 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12930 |
\begin{align*}
y^{\prime \prime }+y \sin \left (x \right )&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| 12931 |
\begin{align*}
y^{\prime }&=f \left (a x +b y+c \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12932 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12933 |
\begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12934 |
\begin{align*}
y^{\prime }&=f \left (a +b x +c y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12935 |
\begin{align*}
x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 12936 |
\begin{align*}
2 \left (x +1\right ) y+2 x \left (-x +2\right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 12937 | \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+2 x \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.776 |
|
| 12938 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12939 |
\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*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 12940 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+\left (x +1\right ) x y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12941 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| 12942 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-3 y_{2}+4 x -2 \\
y_{2}^{\prime }&=y_{1}-2 y_{2}+3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12943 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12944 |
\begin{align*}
x^{4} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }+\left (x^{2}-3 x +2\right ) y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12945 |
\begin{align*}
5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| 12946 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 12947 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 12948 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y-{\mathrm e}^{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 12949 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y^{\prime }+x \left (b \,x^{2} a +b c +2 a \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 12950 |
\begin{align*}
x^{2} \left (a x +b \right ) y^{\prime \prime }+\left (a \left (2-n -m \right ) x^{2}-b \left (n +m \right ) x \right ) y^{\prime }+\left (a m \left (n -1\right ) x +b n \left (m +1\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.777 |
|
| 12951 |
\begin{align*}
\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 12952 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 12953 |
\begin{align*}
y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| 12954 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.777 |
|
| 12955 |
\begin{align*}
t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12956 |
\begin{align*}
y^{\prime }+\left (-1+\frac {1}{x}\right ) y&=-\frac {2}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12957 | \begin{align*}
x_{1}^{\prime }&=x_{1}-{\mathrm e}^{t} \\
x_{2}^{\prime }&=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.778 |
|
| 12958 |
\begin{align*}
x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12959 |
\begin{align*}
x^{\prime }&=z-y \\
y^{\prime }&=z \\
z^{\prime }&=z-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12960 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12961 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.778 |
|
| 12962 |
\begin{align*}
-\frac {u^{\prime \prime }}{2}&=x \\
u \left (0\right ) &= 0 \\
u \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.778 |
|
| 12963 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=t^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| 12964 |
\begin{align*}
6 w^{\prime }-13 w&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12965 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12966 |
\begin{align*}
y^{\prime \prime }+y-\sin \left (n x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12967 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{2}+b x \right ) y^{\prime }-\left (a c \,x^{2}+\left (b c +c^{2}+a \right ) x +b +2 c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.779 |
|
| 12968 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12969 |
\begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12970 |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12971 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\sin \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| 12972 |
\begin{align*}
4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12973 |
\begin{align*}
t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 12974 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 12975 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.780 |
|
| 12976 | \begin{align*}
x^{2} \left (x -y\right ) y^{\prime \prime }&=\left (-y+y^{\prime } x \right )^{2} \\
\end{align*} | ✗ | ✓ | ✓ | ✗ | 0.780 |
|
| 12977 |
\begin{align*}
x^{2} y^{\prime \prime \prime \prime }&=2 y^{\prime \prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12978 |
\begin{align*}
-\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12979 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12980 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12981 |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12982 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+4 y&=2 \sinh \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12983 |
\begin{align*}
x_{1}^{\prime }&=x_{1}+3 x_{3} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= -1 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12984 |
\begin{align*}
y^{\prime \prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| 12985 |
\begin{align*}
3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 12986 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| 12987 |
\begin{align*}
x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 12988 |
\begin{align*}
{y^{\prime \prime }}^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.782 |
|
| 12989 |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }&={\mathrm e}^{-3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 12990 |
\begin{align*}
t^{2} y^{\prime }&=1-2 t y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 12991 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&={\mathrm e}^{-4 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| 12992 |
\begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 12993 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2}+x_{3} \\
x_{2}^{\prime }&=4 x_{1}+3 x_{2}+x_{4} \\
x_{3}^{\prime }&=3 x_{3}-4 x_{4} \\
x_{4}^{\prime }&=4 x_{3}+3 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 12994 |
\begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 12995 | \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). | ✓ | ✓ | ✓ | ✓ | 0.783 |
|
| 12996 |
\begin{align*}
x^{4} y^{\prime \prime }-\left (a +b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) x +a b \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.783 |
|
| 12997 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 12998 |
\begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 12999 |
\begin{align*}
x^{\prime }&=x+2 y+2 t \\
y^{\prime }&=3 y+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| 13000 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.783 |
|