Problems 3301 to 3400

Table 6.67: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

3301	\[ {} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \]	✓	✓	✓

3302	\[ {} 2 x^{2} y+{y^{\prime }}^{2} = x^{3} y^{\prime } \]	✓	✓	✓

3303	\[ {} y {y^{\prime }}^{2} = 3 x y^{\prime }+y \]	✓	✓	✓

3304	\[ {} 8 x +1 = y {y^{\prime }}^{2} \]	✓	✓	✓

3305	\[ {} y {y^{\prime }}^{2}+2 y^{\prime }+1 = 0 \]	✓	✓	✗

3306	\[ {} \left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime } \]	✓	✓	✓

3307	\[ {} x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x = 0 \]	✓	✓	✗

3308	\[ {} y+2 x y^{\prime } = {y^{\prime }}^{2} x \]	✓	✓	✓

3309	\[ {} x = {y^{\prime }}^{2}+y^{\prime } \]	✓	✓	✓

3310	\[ {} x = y-{y^{\prime }}^{3} \]	✓	✓	✓

3311	\[ {} x +2 y y^{\prime } = {y^{\prime }}^{2} x \]	✓	✓	✓

3312	\[ {} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \]	✓	✓	✓

3313	\[ {} x {y^{\prime }}^{3} = y y^{\prime }+1 \]	✓	✓	✗

3314	\[ {} y \left (1+{y^{\prime }}^{2}\right ) = 2 x y^{\prime } \]	✓	✓	✗

3315	\[ {} 2 x +{y^{\prime }}^{2} x = 2 y y^{\prime } \]	✓	✓	✓

3316	\[ {} x = y y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✗

3317	\[ {} 4 {y^{\prime }}^{2} x +2 x y^{\prime } = y \]	✓	✓	✓

3318	\[ {} y = y^{\prime } x \left (y^{\prime }+1\right ) \]	✓	✓	✓

3319	\[ {} 2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2} \]	✓	✓	✗

3320	\[ {} {y^{\prime }}^{3}+x y y^{\prime } = 2 y^{2} \]	✓	✓	✗

3321	\[ {} 3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \]	✗	✓	✗

3322	\[ {} 2 {y^{\prime }}^{5}+2 x y^{\prime } = y \]	✓	✓	✗

3323	\[ {} \frac {1}{{y^{\prime }}^{2}}+x y^{\prime } = 2 y \]	✓	✓	✗

3324	\[ {} 2 y = 3 x y^{\prime }+4+2 \ln \left (y^{\prime }\right ) \]	✓	✓	✗

3325	\[ {} y = x y^{\prime }+{y^{\prime }}^{2} \]	✓	✓	✓

3326	\[ {} y = x y^{\prime }+\frac {1}{y^{\prime }} \]	✓	✓	✗

3327	\[ {} y = x y^{\prime }-\sqrt {y^{\prime }} \]	✓	✓	✓

3328	\[ {} y = x y^{\prime }+\ln \left (y^{\prime }\right ) \]	✓	✓	✓

3329	\[ {} y = x y^{\prime }+\frac {3}{{y^{\prime }}^{2}} \]	✓	✓	✗

3330	\[ {} y = x y^{\prime }-{y^{\prime }}^{{2}/{3}} \]	✓	✓	✗

3331	\[ {} y = x y^{\prime }+{\mathrm e}^{y^{\prime }} \]	✓	✓	✓

3332	\[ {} \left (y-x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2} \]	✓	✓	✗

3333	\[ {} {y^{\prime }}^{2} x -y y^{\prime }-2 = 0 \]	✓	✓	✗

3334	\[ {} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = 0 \]	✓	✓	✓

3335	\[ {} y^{\prime } = \sqrt {1-y} \]	✓	✓	✓

3336	\[ {} y^{\prime } = x y-x^{2} \]	✓	✓	✓

3337	\[ {} y^{\prime } = x^{2} y^{2} \]	✓	✓	✓

3338	\[ {} y^{\prime } = 3 x +\frac {y}{x} \]	✓	✓	✓

3339	\[ {} y^{\prime } = \ln \left (x y\right ) \]	✓	✓	✓

3340	\[ {} y^{\prime } = 1+y^{2} \]	✓	✓	✓

3341	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✓

3342	\[ {} y^{\prime } = \sqrt {1+x y} \]	✓	✓	✓

3343	\[ {} y^{\prime } = \cos \left (x \right )+\sin \left (y\right ) \]	✓	✓	✓

3344	\[ {} y^{\prime \prime }-y = \sin \left (x \right ) \]	✓	✓	✗

3345	\[ {} y^{\prime \prime }-2 y = {\mathrm e}^{2 x} \]	✓	✓	✗

3346	\[ {} y^{\prime \prime }+2 y y^{\prime } = 0 \]	✓	✓	✗

3347	\[ {} y^{\prime \prime } = \sin \left (y\right ) \]	✓	✓	✗

3348	\[ {} y^{\prime \prime }+\frac {{y^{\prime }}^{2}}{2}-y = 0 \]	✓	✓	✗

3349	\[ {} y^{\prime \prime } = \sin \left (x y\right ) \]	✓	✓	✗

3350	\[ {} y^{\prime \prime } = \cos \left (x y\right ) \]	✓	✓	✗

3351	\[ {} 2 x y^{\prime \prime }+5 y^{\prime }+x y = 0 \]	✓	✓	✓

3352	\[ {} 3 x \left (3 x +2\right ) y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]	✓	✓	✓

3353	\[ {} x^{2} \left (x +4\right ) y^{\prime \prime }+7 x y^{\prime }-y = 0 \]	✓	✓	✓

3354	\[ {} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = 0 \]	✓	✓	✓

3355	\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = 0 \]	✓	✓	✓

3356	\[ {} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = 0 \]	✓	✓	✓

3357	\[ {} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = 0 \]	✓	✓	✓

3358	\[ {} 2 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+\left (3 x +2\right ) y = 0 \]	✓	✓	✓

3359	\[ {} 3 x^{2} y^{\prime \prime }+\left (-x^{2}+5 x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = 0 \]	✓	✓	✓

3360	\[ {} 4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y = 0 \]	✓	✓	✓

3361	\[ {} 4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y = 0 \]	✓	✓	✗

3362	\[ {} 9 x^{2} y^{\prime \prime }+9 \left (-x^{2}+x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✓

3363	\[ {} 4 x^{2} \left (1-x \right ) y^{\prime \prime }+3 x \left (2 x +1\right ) y^{\prime }-3 y = 0 \]	✓	✓	✓

3364	\[ {} 2 x^{2} \left (1-3 x \right ) y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \]	✓	✓	✓

3365	\[ {} 4 x^{2} \left (1+x \right ) y^{\prime \prime }-5 x y^{\prime }+2 y = 0 \]	✓	✓	✓

3366	\[ {} x^{2} \left (x +4\right ) y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

3367	\[ {} \left (8-x \right ) x^{2} y^{\prime \prime }+6 x y^{\prime }-y = 0 \]	✓	✓	✓

3368	\[ {} 2 x^{2} y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime }-\left (1+x \right ) y = 0 \]	✓	✓	✓

3369	\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \]	✓	✓	✓

3370	\[ {} 3 x^{2} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

3371	\[ {} x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (1+x \right ) y = 0 \]	✓	✗	✗

3372	\[ {} 2 x y^{\prime \prime }-\left (x^{3}+1\right ) y^{\prime }+y = 0 \]	✓	✓	✓

3373	\[ {} x y^{\prime \prime }+y^{\prime }+2 y = 0 \]	✓	✓	✓

3374	\[ {} x y^{\prime \prime }+y^{\prime }+2 x y = 0 \]	✓	✓	✓

3375	\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (1+x \right ) y = 0 \]	✓	✓	✓

3376	\[ {} x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

3377	\[ {} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+4 y = 0 \]	✓	✓	✓

3378	\[ {} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]	✓	✓	✓

3379	\[ {} x^{2} y^{\prime \prime }+x \left (x^{2}-1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \]	✓	✓	✓

3380	\[ {} x^{2} y^{\prime \prime }+x \left (2 x -1\right ) y^{\prime }+x \left (x -1\right ) y = 0 \]	✓	✓	✓

3381	\[ {} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \]	✓	✓	✓

3382	\[ {} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (3 x^{2}+2\right ) y = 0 \]	✓	✓	✓

3383	\[ {} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-9 y = 0 \]	✓	✓	✓

3384	\[ {} \left (-x^{2}+x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]	✓	✓	✓

3385	\[ {} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0 \]	✓	✓	✗

3386	\[ {} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x -4\right ) y^{\prime }+4 y = 0 \]	✓	✓	✓

3387	\[ {} x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y = 0 \]	✓	✓	✓

3388	\[ {} x y^{\prime \prime }+3 y^{\prime }-y = x \]	✓	✓	✗

3389	\[ {} x y^{\prime \prime }+3 y^{\prime }-y = x \]	✓	✓	✗

3390	\[ {} x y^{\prime \prime }+y^{\prime }-2 x y = x^{2} \]	✓	✓	✗

3391	\[ {} x y^{\prime \prime }-x y^{\prime }+y = x^{3} \]	✓	✓	✗

3392	\[ {} \left (1-2 x \right ) y^{\prime \prime }+4 x y^{\prime }-4 y = x^{2}-x \]	✓	✓	✗

3393	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x \]	✓	✓	✗

3394	\[ {} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x \]	✓	✓	✗

3395	\[ {} 3 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x \]	✓	✓	✗

3396	\[ {} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2} \]	✓	✓	✗

3397	\[ {} 9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = x -1 \]	✓	✓	✗

3398	\[ {} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1 \]	✓	✓	✗

3399	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2} \]	✓	✓	✗

3400	\[ {} \left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2+2 x \right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2} \]	✓	✓	✗

6.34 Problems 3301 to 3400