| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 4101 |
\begin{align*}
\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.321 |
|
| 4102 |
\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.321 |
|
| 4103 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4104 |
\begin{align*}
x^{\prime }-2 x+4 y&=0 \\
3 x+2 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4105 |
\begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4106 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4107 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 4108 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4109 |
\begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| 4110 |
\begin{align*}
y^{\prime \prime }+k^{2} x^{4} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4111 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4112 |
\begin{align*}
\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| 4113 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| 4114 |
\begin{align*}
y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.322 |
|
| 4115 |
\begin{align*}
x^{\prime }&=5 x-4 y \\
y^{\prime }&=x+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4116 |
\begin{align*}
y^{\prime \prime \prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4117 |
\begin{align*}
y^{\prime } x -\sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4118 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }-2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4119 |
\begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4120 |
\begin{align*}
x^{\prime }&=b \,{\mathrm e}^{t} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 4121 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 4122 |
\begin{align*}
4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 4123 |
\begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 4124 |
\begin{align*}
-2 y^{\prime }-\left (x +4\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.323 |
|
| 4125 |
\begin{align*}
4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.323 |
|
| 4126 |
\begin{align*}
\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.323 |
|
| 4127 |
\begin{align*}
x^{2} y^{\prime }-\sqrt {x}&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 4128 |
\begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 4129 |
\begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.323 |
|
| 4130 |
\begin{align*}
\left (x^{2}-3\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4131 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4132 |
\begin{align*}
y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4133 |
\begin{align*}
y^{\prime }&=y x -x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4134 |
\begin{align*}
\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4135 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4136 |
\begin{align*}
x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4137 |
\begin{align*}
a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.324 |
|
| 4138 |
\begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4139 |
\begin{align*}
x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.324 |
|
| 4140 |
\begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}+\left (a y+b x \right ) y^{2}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.324 |
|
| 4141 |
\begin{align*}
2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.324 |
|
| 4142 |
\begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=3 x-2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4143 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 4144 |
\begin{align*}
x^{\prime }&=-3 y \\
y^{\prime }&=3 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4145 |
\begin{align*}
36 y^{\prime }+36 y^{2}-12 y+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4146 |
\begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=F \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4147 |
\begin{align*}
{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4148 |
\begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.325 |
|
| 4149 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.325 |
|
| 4150 |
\begin{align*}
y^{2} y^{\prime \prime }&=8 x^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.325 |
|
| 4151 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4152 |
\begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4153 |
\begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 4154 |
\begin{align*}
x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4155 |
\begin{align*}
4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4156 |
\begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4157 |
\begin{align*}
y^{\prime }&=t^{2}+3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4158 |
\begin{align*}
y_{1}^{\prime }&=4 y_{2} \\
y_{2}^{\prime }&=4 y_{2}-y_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4159 |
\begin{align*}
y^{\prime }&={\mathrm e}^{3 x}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4160 |
\begin{align*}
x^{\prime }&=5 x-2 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4161 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4162 |
\begin{align*}
y^{\prime }&=3 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4163 |
\begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4164 |
\begin{align*}
x^{\prime }&=2 x+\frac {y}{2} \\
y^{\prime }&=-\frac {x}{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4165 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4166 |
\begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4167 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4168 |
\begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| 4169 |
\begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4170 |
\begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4171 |
\begin{align*}
y^{\prime } x&=y \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| 4172 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| 4173 |
\begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| 4174 |
\begin{align*}
\left (x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4175 |
\begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=3 x-4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4176 |
\begin{align*}
y_{1}^{\prime }&=-5 y_{1}+y_{2} \\
y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4177 |
\begin{align*}
x_{1}^{\prime }&=-4 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}-2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4178 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4179 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4180 |
\begin{align*}
x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\
x^{\prime }+3 x+y^{\prime }-7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| 4181 |
\begin{align*}
y^{\prime }&=a t y+q \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| 4182 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-4 x_{2} \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4183 |
\begin{align*}
y^{\prime }-2 y&=x y^{3} \\
y \left (0\right ) &= 2 \sqrt {2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4184 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4185 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4186 |
\begin{align*}
a \,x^{m} y^{n}+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.328 |
|
| 4187 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4188 |
\begin{align*}
y^{\prime } t +y&=0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4189 |
\begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.328 |
|
| 4190 |
\begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4191 |
\begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4192 |
\begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4193 |
\begin{align*}
y^{\prime \prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.328 |
|
| 4194 |
\begin{align*}
y^{\prime }&=x \\
x^{\prime }&=-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4195 |
\begin{align*}
y_{1}^{\prime }&=-y_{1} \\
y_{2}^{\prime }&=3 y_{2} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| 4196 |
\begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-9 x+6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4197 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4198 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4199 |
\begin{align*}
\left (x -2\right ) y^{\prime }&=y x \\
y \left (0\right ) &= 4 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| 4200 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+5 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.329 |
|