4.14.5 Problems 401 to 500

Table 4.1131: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

Sympy

5678

\[ {} 2 {y^{\prime }}^{4}-y y^{\prime }-2 = 0 \]

5679

\[ {} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0 \]

5680

\[ {} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0 \]

5681

\[ {} {y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3} \]

5682

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0 \]

5683

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0 \]

5684

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0 \]

5685

\[ {} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \]

5686

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

5687

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

5689

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

5690

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

5691

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

5692

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

5693

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

5694

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

5695

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

5696

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

5697

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

5698

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

5699

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

5700

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

5701

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

5702

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

5703

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

5704

\[ {} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0 \]

5705

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

5706

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

5707

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

5708

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

5709

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

5710

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

5711

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

5712

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

5713

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

5714

\[ {} \ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

6831

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

6832

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

6833

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

6885

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

6886

\[ {} {y^{\prime }}^{2}-\frac {a^{2}}{x^{2}} = 0 \]

6887

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

6888

\[ {} {y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0 \]

6889

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

6890

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

6891

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

6892

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

6893

\[ {} y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x} = 0 \]

6894

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

6895

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

6896

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

6897

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

6898

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

6899

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

6900

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

6901

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

6902

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

6903

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

6904

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

6905

\[ {} \frac {y-x y^{\prime }}{y^{\prime }+y^{2}} = \frac {y-x y^{\prime }}{1+x^{2} y^{\prime }} \]

7162

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

7163

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

7576

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

7577

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

7858

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

7953

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

7954

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

7955

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

7956

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

7957

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

7958

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

7959

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

7960

\[ {} 16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

7961

\[ {} x {y^{\prime }}^{5}-{y^{\prime }}^{4} y+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0 \]

7962

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

7963

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

7964

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

7965

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

7966

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

7967

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

7968

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

7969

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

7970

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

7971

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

7972

\[ {} \left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y \]

7973

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

7974

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

7975

\[ {} y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y \]

7976

\[ {} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0 \]

7977

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

8169

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

8170

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

8204

\[ {} {y^{\prime }}^{2} = 4 y \]

8205

\[ {} {y^{\prime }}^{2} = 9-y^{2} \]

8207

\[ {} {y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1 \]

8214

\[ {} x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0 \]

8280

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

8291

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

8418

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

8423

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