4.2.20 Problems 1901 to 2000

Table 4.245: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

7789

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

7790

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

7791

\[ {} \frac {x^{\prime \prime }}{2} = -48 x \]

7792

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

7793

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

7794

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

7795

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

7796

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

7797

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

7798

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

7800

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

7801

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

7805

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

7806

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

7807

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

7808

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

7809

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

7816

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

7817

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

7818

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

7819

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

7822

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \]

7823

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

7824

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

7825

\[ {} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

7826

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

7827

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

7828

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

7833

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

7834

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

7835

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

7836

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

7837

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

7838

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

7839

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x} \]

7840

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \]

7844

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

7845

\[ {} q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]

7860

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

7861

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

7862

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

7863

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

7864

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

7865

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

7978

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

7980

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

7981

\[ {} y^{\prime \prime }+9 y = x \cos \left (x \right ) \]

7982

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

7984

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

7988

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

7990

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

7992

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

7993

\[ {} y^{\prime \prime }+25 y = 0 \]

7998

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

7999

\[ {} y^{\prime \prime }-4 y^{\prime } = 5 \]

8003

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

8004

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

8005

\[ {} y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x} \]

8006

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

8007

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

8008

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

8009

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

8010

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

8011

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

8012

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]

8013

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

8014

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

8015

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

8016

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

8017

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

8018

\[ {} y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \]

8020

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

8022

\[ {} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \]

8023

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

8024

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

8027

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

8028

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

8030

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

8031

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

8032

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

8033

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

8034

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

8035

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \]

8036

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

8037

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

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

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