Problems 1 to 100

Table 4.1155: Second order, non-linear and homogeneous


#	ODE	Mathematica	Maple	Sympy

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

151	\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \]	✓	✓	✓

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

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

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

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

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

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

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

2820	\[ {} z^{\prime \prime }+z^{3} = 0 \]	✓	✓	✓

2821	\[ {} z^{\prime \prime }+z+z^{5} = 0 \]	✓	✓	✗

2823	\[ {} z^{\prime \prime }+\frac {z}{1+z^{2}} = 0 \]	✓	✓	✓

2824	\[ {} z^{\prime \prime }+z-2 z^{3} = 0 \]	✓	✓	✗

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

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

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

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

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

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

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

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

6305	\[ {} y^{\prime \prime } = 6 y^{2} \]	✓	✓	✓

6308	\[ {} y^{\prime \prime } = 2 y^{3} \]	✓	✓	✓

6315	\[ {} a \,x^{r} y^{s}+y^{\prime \prime } = 0 \]	✗	✗	✗

6316	\[ {} a \sin \left (y\right )+y^{\prime \prime } = 0 \]	✓	✓	✗

6317	\[ {} a \,{\mathrm e}^{y}+y^{\prime \prime } = 0 \]	✓	✓	✓

6318	\[ {} y^{\prime \prime } = f \left (y\right ) \]	✓	✓	✗

6319	\[ {} y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime } = 2 y^{3} \]	✗	✗	✗

6320	\[ {} y y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

6321	\[ {} y y^{\prime }+y^{\prime \prime } = y^{3} \]	✓	✓	✗

6322	\[ {} a y+y y^{\prime }+y^{\prime \prime } = y^{3} \]	✓	✓	✗

6324	\[ {} 2 a^{2} y+a y^{2}+\left (3 a +y\right ) y^{\prime }+y^{\prime \prime } = y^{3} \]	✓	✓	✗

6325	\[ {} y^{\prime \prime } = f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime } \]	✗	✓	✗

6328	\[ {} y^{\prime \prime } = f^{\prime }\left (x \right ) y+\left (f \left (x \right )-2 y\right ) y^{\prime } \]	✗	✗	✗

6334	\[ {} y^{\prime \prime } = f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime } \]	✗	✓	✗

6335	\[ {} y^{\prime \prime } = a \left (1+2 y y^{\prime }\right ) \]	✓	✓	✗

6336	\[ {} b y+a \left (y^{2}-1\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✗	✗

6337	\[ {} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✗	✗

6339	\[ {} 2 \cot \left (x \right ) y^{\prime }+2 \tan \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6340	\[ {} y^{\prime \prime } = a {y^{\prime }}^{2} \]	✓	✓	✓

6342	\[ {} b y+a {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6343	\[ {} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6344	\[ {} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✗	✗	✗

6345	\[ {} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2} \]	✓	✓	✓

6346	\[ {} f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✓

6347	\[ {} b y+a y {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6348	\[ {} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6349	\[ {} f \left (x \right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6350	\[ {} f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6351	\[ {} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0 \]	✗	✗	✗

6352	\[ {} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime } = 0 \]	✓	✓	✓

6353	\[ {} y^{\prime \prime } = \left (a -x \right ) {y^{\prime }}^{3} \]	✓	✓	✓

6354	\[ {} \left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0 \]	✗	✓	✗

6355	\[ {} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime } = 0 \]	✓	✓	✓

6356	\[ {} a {y^{\prime }}^{3}+y^{\prime \prime } = 0 \]	✓	✓	✓

6357	\[ {} y^{\prime \prime } = x {y^{\prime }}^{3} \]	✓	✓	✓

6358	\[ {} \left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0 \]	✓	✓	✗

6359	\[ {} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime } = 0 \]	✓	✓	✗

6360	\[ {} y^{\prime \prime } = a \left (x y^{\prime }-y\right )^{k} \]	✓	✓	✗

6361	\[ {} g \left (x \right ) y^{\prime }+f \left (x \right ) {y^{\prime }}^{k}+y^{\prime \prime } = 0 \]	✓	✓	✗

6362	\[ {} y^{\prime \prime } = A \,x^{a} y^{b} {y^{\prime }}^{c} \]	✗	✗	✗

6363	\[ {} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}} \]	✓	✓	✓

6364	\[ {} y^{\prime \prime } = a \sqrt {b y^{2}+{y^{\prime }}^{2}} \]	✓	✓	✗

6365	\[ {} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

6366	\[ {} y^{\prime \prime } = a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

6367	\[ {} y^{\prime \prime } = a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

6368	\[ {} y^{\prime \prime } = a y {\left (1+\left (b -y^{\prime }\right )^{2}\right )}^{{3}/{2}} \]	✓	✓	✗

6369	\[ {} y^{\prime \prime } = a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]	✓	✓	✗

6370	\[ {} y^{3} y^{\prime }+y^{\prime \prime } = y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} \]	✓	✓	✗

6371	\[ {} y^{\prime \prime } = f \left (y^{\prime }\right ) \]	✓	✓	✗

6372	\[ {} y^{\prime \prime } = f \left (a x +b y, y^{\prime }\right ) \]	✗	✗	✗

6373	\[ {} y^{\prime \prime } = f \left (x , \frac {y^{\prime }}{y}\right ) y \]	✗	✗	✗

6374	\[ {} y^{\prime \prime } = x^{n -2} f \left (y x^{-n}, x^{-n +1} y^{\prime }\right ) \]	✗	✗	✗

6376	\[ {} 2 y^{\prime \prime } = y \left (a -y^{2}\right ) \]	✓	✓	✗

6377	\[ {} 9 {y^{\prime }}^{4}+8 y^{\prime \prime } = 0 \]	✓	✓	✓

6378	\[ {} a \,{\mathrm e}^{y} x +y^{\prime }+x y^{\prime \prime } = 0 \]	✓	✓	✗

6379	\[ {} x y^{5}+2 y^{\prime }+x y^{\prime \prime } = 0 \]	✓	✓	✗

6380	\[ {} x y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0 \]	✗	✗	✗

6381	\[ {} x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0 \]	✗	✗	✗

6382	\[ {} a \,x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0 \]	✗	✗	✗

6383	\[ {} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0 \]	✗	✗	✗

6385	\[ {} x y^{\prime \prime } = \left (1-y\right ) y^{\prime } \]	✓	✓	✗

6386	\[ {} x {y^{\prime }}^{2}+x y^{\prime \prime } = y^{\prime } \]	✓	✓	✓

4.17.1 Problems 1 to 100