4.15.1 Problems 1 to 58

Table 4.1151: Higher order, non-linear and homogeneous

#

ODE

Mathematica

Maple

Sympy

6724

\[ {} -6 y+6 y^{\prime } \left (1+x \right )-3 x \left (x +2\right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime } = 0 \]

6760

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

6800

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

6801

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

6802

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

6804

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

6805

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

6806

\[ {} 3 y^{\prime } y^{\prime \prime }+\left (a +y\right ) y^{\prime \prime \prime } = 0 \]

6807

\[ {} 3 y^{2}+18 y y^{\prime } x +9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime } = 0 \]

6808

\[ {} 2 {y^{\prime }}^{3}+3 y^{\prime \prime }+6 y y^{\prime } y^{\prime \prime }+\left (x +y^{2}\right ) y^{\prime \prime \prime } = 0 \]

6809

\[ {} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0 \]

6810

\[ {} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0 \]

6811

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

6813

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

6814

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

6815

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

6818

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

6821

\[ {} \sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right ) = y^{\prime \prime } y^{\prime \prime \prime } \]

6822

\[ {} 3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 5 {y^{\prime \prime \prime }}^{2} \]

6823

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

8163

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

8812

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

8839

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

13061

\[ {} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0 \]

13063

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

13064

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

13066

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

13067

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

13068

\[ {} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0 \]

13069

\[ {} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0 \]

13071

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

13072

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

13073

\[ {} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} = 0 \]

13074

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

13075

\[ {} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

13076

\[ {} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0 \]

13078

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

14284

\[ {} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2} = 0 \]

15220

\[ {} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

15522

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

15523

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

16513

\[ {} y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }} \]

16558

\[ {} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \]

18214

\[ {} y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}} \]

18225

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

18238

\[ {} y^{\prime \prime \prime } = 3 y y^{\prime } \]

19258

\[ {} a^{3} y^{\prime \prime \prime } y^{\prime \prime } = \sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \]

19259

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

19261

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

19275

\[ {} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 0 \]

19276

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

19898

\[ {} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0 \]

19900

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

20650

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

22073

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

22611

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

23585

\[ {} 3 x y^{\prime \prime \prime }-4 x y = \cos \left (y\right ) \]

25261

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