Problems 401 to 500

Table 4.553: Second ODE homogeneous ODE


#	ODE	Mathematica	Maple	Sympy

3100	\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]	✓	✓	✓

3221	\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0 \]	✓	✓	✓

3222	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0 \]	✓	✓	✓

3223	\[ {} 4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0 \]	✓	✓	✓

3224	\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0 \]	✓	✓	✓

3245	\[ {} y^{\prime \prime } = k^{2} y \]	✓	✓	✓

3246	\[ {} x^{\prime \prime }+k^{2} x = 0 \]	✓	✓	✓

3248	\[ {} x^{\prime \prime } = \frac {k^{2}}{x^{2}} \]	✓	✓	✓

3250	\[ {} \left (1-x \right ) y^{\prime \prime } = y^{\prime } \]	✓	✓	✓

3251	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0 \]	✓	✓	✓

3252	\[ {} y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime } \]	✓	✓	✓

3258	\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✗

3259	\[ {} y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime } \]	✓	✓	✓

3260	\[ {} y^{\prime \prime } = y y^{\prime } \]	✓	✓	✗

3262	\[ {} y^{\prime \prime }+y y^{\prime } = 0 \]	✓	✓	✗

3263	\[ {} y^{\prime \prime }+2 {y^{\prime }}^{2} = 0 \]	✓	✓	✓

3264	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]	✓	✓	✗

3266	\[ {} y^{\prime \prime } = y \]	✓	✓	✓

3267	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime } \]	✓	✓	✗

3268	\[ {} 2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

3270	\[ {} y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3} \]	✓	✓	✓

3271	\[ {} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \]	✓	✓	✗

3273	\[ {} 2 y^{\prime \prime } = {\mathrm e}^{y} \]	✓	✓	✗

3274	\[ {} y^{\prime \prime } = y^{3} \]	✓	✓	✗

3275	\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right ) \]	✗	✗	✗

3276	\[ {} y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2} \]	✓	✓	✗

3278	\[ {} y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2} \]	✗	✓	✗

3279	\[ {} \left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime } \]	✗	✓	✗

3280	\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right ) \]	✓	✗	✗

3281	\[ {} 2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2} \]	✓	✓	✗

3282	\[ {} x^{\prime \prime }-k^{2} x = 0 \]	✓	✓	✓

3283	\[ {} y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2} \]	✓	✓	✗

3284	\[ {} \left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime } \]	✓	✓	✓

3483	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0 \]	✓	✓	✓

3485	\[ {} f^{\prime \prime }+2 f^{\prime }+5 f = 0 \]	✓	✓	✓

3495	\[ {} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0 \]	✓	✓	✗

3558	\[ {} y^{\prime \prime }-25 y = 0 \]	✓	✓	✓

3559	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

3560	\[ {} y^{\prime \prime }+y^{\prime }-2 y = 0 \]	✓	✓	✓

3563	\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]	✓	✓	✓

3564	\[ {} y^{\prime \prime }-9 y = 0 \]	✓	✓	✓

3565	\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]	✓	✓	✓

3566	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]	✓	✓	✓

3567	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]	✓	✓	✓

3570	\[ {} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+b y a = 0 \]	✓	✓	✓

3571	\[ {} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0 \]	✓	✓	✓

3572	\[ {} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0 \]	✓	✓	✓

3573	\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]	✓	✓	✓

3574	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]	✓	✓	✓

3575	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]	✓	✓	✓

3576	\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]	✓	✓	✓

3590	\[ {} y^{\prime \prime }+y^{\prime }-6 y = 0 \]	✓	✓	✓

3591	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0 \]	✓	✓	✓

3696	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]	✓	✓	✓

3697	\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]	✓	✓	✓

3698	\[ {} y^{\prime \prime }-36 y = 0 \]	✓	✓	✓

3699	\[ {} y^{\prime \prime }+4 y^{\prime } = 0 \]	✓	✓	✓

3707	\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \]	✓	✓	✓

3708	\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]	✓	✓	✓

3781	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0 \]	✓	✓	✓

3782	\[ {} t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0 \]	✓	✓	✓

3783	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]	✓	✓	✓

3784	\[ {} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✗

3785	\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \]	✓	✓	✓

3786	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✗

3787	\[ {} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0 \]	✓	✓	✓

3788	\[ {} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \]	✓	✓	✓

3935	\[ {} y^{\prime \prime }+y^{\prime }-2 y = 0 \]	✓	✓	✓

3936	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

3955	\[ {} y^{\prime \prime }-y = 0 \]	✓	✓	✓

4118	\[ {} y^{\prime \prime }+8 y^{\prime }+15 y = 0 \]	✓	✓	✓

4119	\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]	✓	✓	✓

4120	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]	✓	✓	✓

4121	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]	✓	✓	✓

4122	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]	✓	✓	✓

4123	\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]	✓	✓	✓

4124	\[ {} 2 y^{\prime \prime }+3 y^{\prime } = 0 \]	✓	✓	✓

4125	\[ {} y^{\prime \prime }+25 y = 0 \]	✓	✓	✓

4126	\[ {} 4 y^{\prime \prime }+y^{\prime }+y = 0 \]	✓	✓	✓

4127	\[ {} y^{\prime \prime } = 0 \]	✓	✓	✓

4128	\[ {} y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]	✓	✓	✓

4139	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]	✓	✓	✗

4161	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]	✓	✓	✓

4163	\[ {} 25 y^{\prime \prime }-30 y^{\prime }+9 y = 0 \]	✓	✓	✓

4407	\[ {} y y^{\prime \prime }-y y^{\prime } = {y^{\prime }}^{2} \]	✓	✓	✗

4432	\[ {} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0 \]	✓	✓	✗

4436	\[ {} \left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0 \]	✓	✓	✗

5715	\[ {} y^{\prime \prime } = 0 \]	✓	✓	✓

5720	\[ {} y^{\prime \prime }+y = 0 \]	✓	✓	✓

5721	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

5735	\[ {} -2 y+y^{\prime \prime } = 0 \]	✓	✓	✓

5737	\[ {} y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

5747	\[ {} y^{\prime \prime }+x y = 0 \]	✓	✓	✓

5748	\[ {} \left (b x +a \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✓

5749	\[ {} \left (x^{2}+a \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5750	\[ {} \left (-x^{2}+a \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5751	\[ {} y^{\prime \prime } = \left (x^{2}+a \right ) y \]	✓	✓	✗

5752	\[ {} \left (b^{2} x^{2}+a \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5753	\[ {} \left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5754	\[ {} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

4.4.5 Problems 401 to 500