4.24.29 Problems 2801 to 2900

Table 4.1067: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

12896

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

12897

\[ {} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \]

12898

\[ {} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}} \]

12899

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

12900

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

12901

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

12902

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

12903

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

12904

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0 \]

12905

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

12906

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

12907

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

12908

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

12909

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

12910

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

12911

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

12913

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

12914

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

12915

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

12916

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

12917

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

12918

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

12919

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

12920

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

12921

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

12922

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

12923

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

12924

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

12925

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

12926

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

12927

\[ {} x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

12928

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

12929

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

12930

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

12931

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

12932

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

12933

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

12934

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

12935

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

12936

\[ {} \left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \]

12937

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

12938

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

12939

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

12940

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

12941

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

12942

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

12943

\[ {} 4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \]

12944

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

12953

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

12964

\[ {} x^{\prime }+t x^{\prime \prime } = 1 \]

12993

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

13075

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

13076

\[ {} x^{\prime \prime } = \frac {4 x}{t^{2}} \]

13077

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

13078

\[ {} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \]

13079

\[ {} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

13080

\[ {} t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \]

13081

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

13082

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

13083

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

13087

\[ {} t^{2} x^{\prime \prime }-2 x = t^{3} \]

13090

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

13091

\[ {} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

13093

\[ {} x^{\prime \prime }+t x^{\prime }+x = 0 \]

13094

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

13096

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

13097

\[ {} t^{2} x^{\prime \prime }+t x^{\prime }+\left (t^{2}-\frac {1}{4}\right ) x = 0 \]

13170

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

13178

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

13189

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

13312

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

13315

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

13316

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

13319

\[ {} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \]

13320

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

13321

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

13322

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

13323

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

13324

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

13325

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

13444

\[ {} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

13445

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

13446

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

13447

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

13448

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

13449

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

13450

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

13452

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

13453

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

13454

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

13455

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

13456

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

13457

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

13458

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

13459

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

13460

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

13461

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

13462

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

13463

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

13464

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