Problems 1 to 100

Table 4.885: Second order, non-linear and non-homogeneous


#	ODE	Mathematica	Maple	Sympy

156	\[ {} y^{3} y^{\prime \prime } = 1 \]	✓	✓	✓

232	\[ {} y y^{\prime \prime } = 6 x^{4} \]	✗	✗	✗

1360	\[ {} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \]	✗	✗	✗

2822	\[ {} z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1 \]	✓	✓	✗

3247	\[ {} y^{3} y^{\prime \prime }+4 = 0 \]	✓	✓	✗

3256	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

3261	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

3265	\[ {} y y^{\prime \prime }+1 = {y^{\prime }}^{2} \]	✓	✓	✗

3269	\[ {} y^{\prime \prime }+2 {y^{\prime }}^{2} = 2 \]	✓	✓	✗

3277	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

3492	\[ {} \frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2} \]	✓	✓	✗

5996	\[ {} y^{3} y^{\prime \prime } = k \]	✓	✓	✓

5997	\[ {} y y^{\prime \prime } = {y^{\prime }}^{2}-1 \]	✓	✓	✗

6008	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

6191	\[ {} k = \frac {y^{\prime \prime }}{\left (y^{\prime }+1\right )^{{3}/{2}}} \]	✓	✓	✗

6235	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0 \]	✓	✓	✗

6698	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✓

6699	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 2 \]	✓	✓	✗

6772	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✓

6782	\[ {} \left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2 \]	✓	✓	✗

7765	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

7824	\[ {} y^{\prime \prime } y^{\prime } = \left (1+x \right ) x \]	✓	✓	✓

7909	\[ {} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✗

7915	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

7916	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

8514	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

8523	\[ {} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2} \]	✓	✓	✓

8524	\[ {} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0 \]	✗	✓	✗

8527	\[ {} 3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \]	✓	✓	✗

8528	\[ {} 4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3 \]	✓	✓	✗

8774	\[ {} y y^{\prime \prime } = 1 \]	✓	✓	✓

8775	\[ {} y y^{\prime \prime } = x \]	✗	✗	✗

8776	\[ {} y^{2} y^{\prime \prime } = x \]	✗	✓	✗

8778	\[ {} 3 y y^{\prime \prime } = \sin \left (x \right ) \]	✗	✗	✗

8779	\[ {} 3 y y^{\prime \prime }+y = 5 \]	✓	✓	✗

8780	\[ {} a y y^{\prime \prime }+b y = c \]	✓	✓	✗

8781	\[ {} a y^{2} y^{\prime \prime }+b y^{2} = c \]	✓	✓	✓

8803	\[ {} y^{\prime \prime }-y y^{\prime } = 2 x \]	✓	✓	✗

8879	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

8880	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x \]	✗	✓	✗

9087	\[ {} {y^{\prime \prime }}^{2}+y^{\prime } = 1 \]	✓	✓	✓

9088	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]	✓	✓	✗

9090	\[ {} {y^{\prime \prime }}^{2}+y^{\prime } = x \]	✓	✓	✗

9091	\[ {} y^{\prime \prime }+{y^{\prime }}^{2} = x \]	✓	✓	✗

11553	\[ {} y^{\prime \prime }-6 y^{2}-x = 0 \]	✗	✗	✗

11555	\[ {} y^{\prime \prime }+a y^{2}+b x +c = 0 \]	✗	✗	✗

11556	\[ {} y^{\prime \prime }-2 y^{3}-x y+a = 0 \]	✗	✗	✗

11558	\[ {} y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0 \]	✗	✗	✗

11559	\[ {} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0 \]	✗	✗	✗

11560	\[ {} y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \]	✓	✓	✗

11568	\[ {} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0 \]	✗	✗	✗

11569	\[ {} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0 \]	✗	✗	✗

11578	\[ {} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0 \]	✗	✗	✗

11585	\[ {} y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 y a^{2}-b = 0 \]	✓	✓	✗

11598	\[ {} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b \]	✓	✓	✗

11613	\[ {} x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0 \]	✓	✓	✗

11618	\[ {} x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0 \]	✓	✓	✗

11619	\[ {} x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0 \]	✗	✗	✗

11621	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

11624	\[ {} x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \]	✓	✗	✗

11626	\[ {} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0 \]	✗	✗	✗

11627	\[ {} 2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0 \]	✗	✗	✗

11634	\[ {} y y^{\prime \prime }-a = 0 \]	✓	✓	✗

11635	\[ {} y y^{\prime \prime }-a x = 0 \]	✗	✗	✗

11636	\[ {} y y^{\prime \prime }-a \,x^{2} = 0 \]	✗	✗	✗

11637	\[ {} y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0 \]	✓	✓	✗

11638	\[ {} y y^{\prime \prime }+y^{2}-a x -b = 0 \]	✓	✗	✗

11640	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

11641	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \]	✓	✓	✗

11660	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0 \]	✓	✓	✗

11665	\[ {} 2 y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

11666	\[ {} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0 \]	✓	✓	✗

11667	\[ {} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a = 0 \]	✗	✗	✗

11672	\[ {} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0 \]	✗	✗	✗

11675	\[ {} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0 \]	✗	✗	✗

11681	\[ {} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

11682	\[ {} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0 \]	✓	✓	✗

11690	\[ {} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0 \]	✓	✓	✗

11694	\[ {} x y y^{\prime \prime }+{y^{\prime }}^{2} x +a y y^{\prime }+f \left (x \right ) = 0 \]	✓	✓	✗

11711	\[ {} y^{2} y^{\prime \prime }-a = 0 \]	✓	✓	✓

11712	\[ {} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0 \]	✗	✓	✗

11713	\[ {} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0 \]	✗	✓	✗

11726	\[ {} x y^{2} y^{\prime \prime }-a = 0 \]	✓	✓	✗

11730	\[ {} y^{3} y^{\prime \prime }-a = 0 \]	✓	✓	✓

11732	\[ {} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0 \]	✗	✗	✗

11733	\[ {} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0 \]	✗	✗	✗

11739	\[ {} \sqrt {y}\, y^{\prime \prime }-a = 0 \]	✓	✓	✗

11750	\[ {} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0 \]	✓	✓	✗

11751	\[ {} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0 \]	✓	✓	✗

11752	\[ {} {y^{\prime \prime }}^{2}-a y-b = 0 \]	✓	✓	✗

11757	\[ {} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0 \]	✗	✗	✗

12232	\[ {} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )} \]	✓	✓	✗

12322	\[ {} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \]	✗	✗	✗

12917	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

12921	\[ {} \left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2} \]	✓	✓	✗

12923	\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✗

12941	\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]	✓	✓	✓

12948	\[ {} x \left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2} x +4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0 \]	✓	✓	✗

12949	\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]	✓	✓	✓

13837	\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0 \]	✓	✓	✓

4.18.1 Problems 1 to 100