4.24.15 Problems 1401 to 1500

Table 4.1381: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

7386

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

7388

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

7390

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

7632

\[ {} y^{\prime \prime }+\operatorname {dif} \left (y, t\right )-6 y = 0 \]

7695

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

7696

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

7697

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

7698

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

7699

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

7700

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

7701

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

7702

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

7705

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

7819

\[ {} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right ) \]

7827

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

7828

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

7861

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

7982

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

7983

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

7984

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

7985

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

7986

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

7987

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

8036

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

8037

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

8038

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

8039

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

8040

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

8041

\[ {} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 6 x \]

8042

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

8043

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

8044

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

8045

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

8046

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

8047

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

8048

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

8049

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

8050

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

8051

\[ {} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

8052

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

8053

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

8054

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

8055

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

8056

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

8057

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

8058

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

8059

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

8060

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

8062

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

8063

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

8064

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

8065

\[ {} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

8066

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

8067

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

8068

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

8069

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

8070

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

8071

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

8072

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

8162

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

8163

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

8164

\[ {} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

8165

\[ {} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

8166

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

8167

\[ {} R^{\prime \prime } = -\frac {k}{R^{2}} \]

8168

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

8185

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

8196

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

8197

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

8198

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

8199

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

8218

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]

8265

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

8273

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

8284

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

8285

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

8288

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

8292

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

8765

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

8766

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

8767

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

8768

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

8769

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

8770

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

8771

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

8772

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

8773

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

8774

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

8775

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

8776

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

8777

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

8778

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

8779

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

8780

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

8781

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

8782

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

8783

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

8784

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

8785

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

8786

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