Problems 2101 to 2200

Table 4.407: Second order ode


#	ODE	Mathematica	Maple	Sympy

7165	\[ {} \left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2} \]	✓	✓	✗

7211	\[ {} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}} = 0 \]	✓	✓	✓

7212	\[ {} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]	✓	✓	✓

7213	\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]	✓	✓	✓

7214	\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]	✓	✓	✓

7215	\[ {} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]	✓	✓	✓

7216	\[ {} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]	✓	✓	✓

7217	\[ {} -a^{2} y+y^{\prime \prime } = \frac {6 y}{x^{2}} \]	✓	✓	✓

7218	\[ {} y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]	✓	✓	✓

7219	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]	✓	✓	✓

7220	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]	✓	✓	✓

7221	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]	✓	✓	✓

7222	\[ {} y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \]	✓	✓	✗

7223	\[ {} y^{\prime \prime }+y \,{\mathrm e}^{2 x} = n^{2} y \]	✓	✓	✗

7224	\[ {} y^{\prime \prime }+\frac {y}{4 x} = 0 \]	✓	✓	✓

7225	\[ {} x y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

7226	\[ {} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \]	✓	✓	✓

7270	\[ {} y^{\prime \prime }+y^{\prime }-2 y = 0 \]	✓	✓	✓

7271	\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]	✓	✓	✓

7272	\[ {} y^{\prime \prime }+9 y^{\prime } = 0 \]	✓	✓	✓

7273	\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 0 \]	✓	✓	✓

7274	\[ {} y^{\prime \prime }-2 y^{\prime }+6 y = 0 \]	✓	✓	✓

7275	\[ {} y^{\prime \prime }+16 y = 0 \]	✓	✓	✓

7276	\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]	✓	✓	✓

7277	\[ {} y^{\prime \prime }+5 y^{\prime } = 0 \]	✓	✓	✓

7278	\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]	✓	✓	✓

7279	\[ {} 2 y^{\prime \prime }+y^{\prime }-y = 0 \]	✓	✓	✓

7280	\[ {} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]	✓	✓	✓

7281	\[ {} y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0 \]	✓	✓	✓

7286	\[ {} y^{\prime \prime }-4 y^{\prime } = 10 \]	✓	✓	✓

7287	\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 16 \]	✓	✓	✓

7288	\[ {} y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x} \]	✓	✓	✓

7289	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]	✓	✓	✓

7290	\[ {} y^{\prime \prime }+y = 2 \,{\mathrm e}^{x} \]	✓	✓	✓

7291	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x} \]	✓	✓	✓

7292	\[ {} y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x} \]	✓	✓	✓

7293	\[ {} y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]	✓	✓	✓

7294	\[ {} y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x} \]	✓	✓	✓

7295	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x} \]	✓	✓	✓

7296	\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]	✓	✓	✓

7297	\[ {} y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]	✓	✓	✓

7298	\[ {} y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \]	✓	✓	✓

7299	\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]	✓	✓	✓

7300	\[ {} 5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]	✓	✓	✓

7301	\[ {} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]	✓	✓	✓

7302	\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]	✓	✓	✓

7303	\[ {} y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]	✓	✓	✓

7304	\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]	✓	✓	✓

7305	\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]	✓	✓	✓

7306	\[ {} 5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x \]	✓	✓	✓

7307	\[ {} 2 y^{\prime \prime }+y^{\prime } = 2 x \]	✓	✓	✓

7308	\[ {} y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x} \]	✓	✓	✓

7309	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x} \]	✓	✓	✓

7310	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]	✓	✓	✓

7311	\[ {} y^{\prime \prime }+y = 8 x \sin \left (x \right ) \]	✓	✓	✓

7312	\[ {} y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x} \]	✓	✓	✓

7313	\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5 \]	✓	✓	✓

7314	\[ {} y^{\prime \prime }-y = \sinh \left (x \right ) \]	✓	✓	✓

7315	\[ {} y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right ) \]	✓	✓	✓

7316	\[ {} y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \]	✓	✓	✓

7317	\[ {} y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]	✓	✓	✓

7318	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✗	✓	✗

7319	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✗	✓	✗

7320	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✗	✓	✗

7321	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✗	✓	✗

7322	\[ {} y^{\prime \prime }+2 x y^{\prime } = 0 \]	✓	✓	✓

7323	\[ {} 2 y y^{\prime \prime } = {y^{\prime }}^{2} \]	✓	✓	✗

7324	\[ {} x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \]	✓	✓	✓

7325	\[ {} {y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right ) \]	✓	✓	✗

7326	\[ {} k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}} \]	✓	✓	✗

7327	\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \]	✓	✓	✓

7328	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \]	✓	✓	✓

7329	\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]	✓	✓	✓

7330	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+6 y = 0 \]	✓	✓	✓

7331	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]	✓	✓	✓

7332	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x} \]	✓	✓	✓

7333	\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]	✓	✓	✓

7334	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right ) \]	✓	✓	✓

7335	\[ {} x^{2} y^{\prime \prime }+y = 3 x^{2} \]	✓	✓	✓

7336	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x \]	✓	✓	✓

7337	\[ {} \left (2-x \right ) x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]	✓	✓	✗

7338	\[ {} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

7339	\[ {} x y^{\prime \prime }-2 y^{\prime } \left (1+x \right )+\left (x +2\right ) y = 0 \]	✓	✓	✗

7340	\[ {} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0 \]	✓	✓	✗

7341	\[ {} x^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )-y = 0 \]	✓	✓	✗

7342	\[ {} x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0 \]	✓	✓	✗

7346	\[ {} r^{\prime \prime }-6 r^{\prime }+9 r = 0 \]	✓	✓	✓

7348	\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \]	✓	✓	✓

7350	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = x \]	✓	✓	✓

7354	\[ {} x y^{\prime \prime }+y^{\prime } = 4 x \]	✓	✓	✓

7355	\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 26 \,{\mathrm e}^{3 x} \]	✓	✓	✓

7356	\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]	✓	✓	✓

7357	\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x} \]	✓	✓	✓

7358	\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x} \]	✓	✓	✓

7362	\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]	✓	✓	✓

7366	\[ {} x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y y^{\prime } \]	✓	✓	✗

7369	\[ {} y^{\prime \prime }+y^{\prime }-6 y = 6 \]	✓	✓	✓

7370	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0 \]	✓	✓	✗

7378	\[ {} y^{\prime \prime } = -4 y \]	✓	✓	✓

7380	\[ {} y^{\prime \prime } = y \]	✓	✓	✓

4.3.22 Problems 2101 to 2200