4.6.6 Problems 501 to 600

Table 4.735: Second order non-linear ODE

#

ODE

Mathematica

Maple

Sympy

10434

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

10435

\[ {} 10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0 \]

10436

\[ {} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )} = 0 \]

10459

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

12850

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

12851

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

12852

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

12853

\[ {} y^{\prime \prime }-6 y^{2}+4 y = 0 \]

12854

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

12855

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

12856

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

12857

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

12858

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

12859

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

12860

\[ {} y^{\prime \prime }+a \,x^{r} y^{2} = 0 \]

12861

\[ {} y^{\prime \prime }+6 a^{10} y^{11}-y = 0 \]

12862

\[ {} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0 \]

12863

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

12864

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

12865

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

12866

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

12867

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

12868

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

12869

\[ {} y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \]

12870

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

12871

\[ {} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0 \]

12872

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

12873

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

12874

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

12875

\[ {} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0 \]

12876

\[ {} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0 \]

12877

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

12878

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

12879

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

12880

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

12881

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

12882

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

12883

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

12884

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

12885

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

12886

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

12887

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

12888

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

12889

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

12890

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

12891

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

12892

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

12893

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

12894

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

12895

\[ {} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0 \]

12896

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

12897

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

12898

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

12899

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

12900

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

12901

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

12902

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

12903

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

12904

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

12905

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

12906

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

12907

\[ {} x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0 \]

12908

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

12909

\[ {} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0 \]

12910

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

12911

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

12912

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

12913

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

12914

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

12915

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

12917

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

12918

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

12919

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

12920

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

12921

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

12922

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

12923

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

12924

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

12925

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

12926

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

12927

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

12928

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

12929

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

12930

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

12931

\[ {} \sqrt {x}\, y^{\prime \prime }-y^{{3}/{2}} = 0 \]

12932

\[ {} \left (x^{2} a +b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {x^{2} a +b x +c}}\right ) = 0 \]

12933

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

12934

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

12935

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

12936

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

12937

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

12938

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

12939

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

12940

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

12941

\[ {} y y^{\prime \prime }-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0 \]

12942

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

12943

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

12944

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

12945

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

12946

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