| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 8801 |
\begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| 8802 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| 8803 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| 8804 |
\begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.882 |
|
| 8805 |
\begin{align*}
y^{\prime \prime }&=\frac {y}{{\mathrm e}^{x}+1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.882 |
|
| 8806 |
\begin{align*}
y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.882 |
|
| 8807 |
\begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.882 |
|
| 8808 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| 8809 |
\begin{align*}
t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| 8810 |
\begin{align*}
y^{\prime \prime } x +\left (1-{\mathrm e}^{x}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| 8811 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| 8812 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\
x_{2}^{\prime }&=3 x_{2}-5 x_{3}+3 x_{4} \\
x_{3}^{\prime }&=-13 x_{2}+22 x_{3}-12 x_{4} \\
x_{4}^{\prime }&=-27 x_{2}+45 x_{3}-25 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| 8813 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| 8814 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| 8815 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8816 |
\begin{align*}
y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8817 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8818 |
\begin{align*}
x_{1}^{\prime }&=x_{1} \\
x_{2}^{\prime }&=3 x_{1}+x_{2}-2 x_{3} \\
x_{3}^{\prime }&=2 x_{1}+2 x_{2}+x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8819 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8820 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.885 |
|
| 8821 |
\begin{align*}
4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8822 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8823 |
\begin{align*}
x^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| 8824 |
\begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| 8825 |
\begin{align*}
x {y^{\prime }}^{n}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.887 |
|
| 8826 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.887 |
|
| 8827 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| 8828 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}+5 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=-6 x_{1}-6 x_{2}-5 x_{3} \\
x_{3}^{\prime }&=6 x_{1}+6 x_{2}+5 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| 8829 |
\begin{align*}
s^{\prime }&=k s \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| 8830 |
\begin{align*}
x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.888 |
|
| 8831 |
\begin{align*}
x^{2} y^{\prime \prime }-\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}}&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
0.888 |
|
| 8832 |
\begin{align*}
x&={y^{\prime }}^{3}-y^{\prime }+2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| 8833 |
\begin{align*}
\left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| 8834 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| 8835 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| 8836 |
\begin{align*}
4 {y^{\prime }}^{2} x \left (x -a \right ) \left (x -b \right )&=\left (3 x^{2}-2 \left (a +b \right ) x +a b \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| 8837 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-2 y-5 z+3 \\
z^{\prime }&=y+2 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.889 |
|
| 8838 |
\begin{align*}
y^{\prime }&=2 y-4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| 8839 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| 8840 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| 8841 |
\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*} |
✓ |
✓ |
✓ |
✗ |
0.890 |
|
| 8842 |
\begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| 8843 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+7 \,{\mathrm e}^{x} y^{\prime } x +9 \left (1+\tan \left (x \right )\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8844 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8845 |
\begin{align*}
2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.891 |
|
| 8846 |
\begin{align*}
y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8847 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8848 |
\begin{align*}
x^{\prime }&=x+z \\
y^{\prime }&=x+y \\
z^{\prime }&=-2 x-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8849 |
\begin{align*}
x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.891 |
|
| 8850 |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8851 |
\begin{align*}
6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8852 |
\begin{align*}
y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| 8853 |
\begin{align*}
x^{\prime }&=2 x-3 y+2 \sin \left (2 t \right ) \\
y^{\prime }&=x-2 y-\cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| 8854 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -4 \\
x_{2} \left (0\right ) &= 4 \\
x_{3} \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| 8855 |
\begin{align*}
4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| 8856 |
\begin{align*}
2 y^{\prime \prime } x +5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.892 |
|
| 8857 |
\begin{align*}
x^{\prime }+5 x&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| 8858 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.892 |
|
| 8859 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.892 |
|
| 8860 |
\begin{align*}
8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.893 |
|
| 8861 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.893 |
|
| 8862 |
\begin{align*}
\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| 8863 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| 8864 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| 8865 |
\begin{align*}
2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.894 |
|
| 8866 |
\begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| 8867 |
\begin{align*}
y^{\prime \prime }&=\left (x^{2}+3\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.894 |
|
| 8868 |
\begin{align*}
4 y^{\prime \prime }+9 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| 8869 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.894 |
|
| 8870 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| 8871 |
\begin{align*}
y^{\prime }+2 y&=1 \\
y \left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| 8872 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| 8873 |
\begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| 8874 |
\begin{align*}
x^{\prime \prime }-x+3 x^{2}&=0 \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.895 |
|
| 8875 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3+t +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| 8876 |
\begin{align*}
y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| 8877 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| 8878 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.896 |
|
| 8879 |
\begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| 8880 |
\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 \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| 8881 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.897 |
|
| 8882 |
\begin{align*}
x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8883 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8884 |
\begin{align*}
3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\
4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8885 |
\begin{align*}
\sqrt {a^{2}-x^{2}}\, \left (-y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime }\right )&=b x {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.898 |
|
| 8886 |
\begin{align*}
2 y+y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8887 |
\begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=x+2 y+z \\
z^{\prime }&=3 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8888 |
\begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
0.898 |
|
| 8889 |
\begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8890 |
\begin{align*}
y^{\prime }&=1+\cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8891 |
\begin{align*}
y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8892 |
\begin{align*}
y^{\prime }-3 y&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| 8893 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| 8894 |
\begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| 8895 |
\begin{align*}
x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\
x+y^{\prime }-y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| 8896 |
\begin{align*}
\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| 8897 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}-\sin \left (x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| 8898 |
\begin{align*}
9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.899 |
|
| 8899 |
\begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| 8900 |
\begin{align*}
4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.901 |
|