5.24.7 Problems 601 to 700

Table 5.1027: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

7683

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

7684

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

7685

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

7686

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

7695

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

7697

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

7698

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

7699

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

7700

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

7701

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

7702

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \]

7703

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

7704

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

7705

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

7706

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

7707

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

7760

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

7761

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

7763

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

7764

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

7765

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

7766

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

7767

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

7768

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

7824

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

7905

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

7906

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

7908

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

7909

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

7910

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

7911

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

7912

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

7913

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

7914

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

7915

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

7916

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

7933

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

7934

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

7935

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

7936

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

7961

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

7962

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

7963

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

7964

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

7965

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

7966

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

7967

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

7968

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

7969

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

8000

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

8001

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

8002

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

8003

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

8004

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

8007

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

8008

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

8009

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

8010

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

8011

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

8012

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

8013

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

8014

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

8015

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

8035

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

8036

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

8037

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

8038

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

8061

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

8067

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

8071

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

8287

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \]

8288

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

8289

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

8290

\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]

8291

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

8292

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

8293

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]

8294

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

8295

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

8296

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

8297

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

8298

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

8299

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

8300

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

8301

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

8302

\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \]

8303

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

8304

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

8305

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

8306

\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]

8308

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

8309

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

8310

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

8362

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

8363

\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \]

8489

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

8490

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

8491

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

8492

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

8493

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