4.5.10 Problems 901 to 1000

Table 4.667: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

7348

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

7350

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

7354

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

7355

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 26 \,{\mathrm e}^{3 x} \]

7356

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

7357

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 6 \,{\mathrm e}^{2 x} \]

7358

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

7362

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right ) \]

7369

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

7370

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

7586

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

7587

\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (3 t \right ) \]

7588

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = -50 \sin \left (5 t \right ) \]

7589

\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \]

7590

\[ {} m y^{\prime \prime }+b y^{\prime }+k y = \cos \left (\omega t \right ) \]

7591

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y = \cos \left (\omega t \right ) \]

7592

\[ {} y^{\prime \prime }+25 y = \cos \left (\omega t \right ) \]

7681

\[ {} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

7682

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

7683

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

7684

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

7685

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

7766

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 8 \]

7767

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

7768

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

7769

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

7770

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

7771

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \]

7772

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

7773

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

7774

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

7775

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

7776

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

7777

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

7778

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

7779

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

7780

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

7781

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

7782

\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \]

7783

\[ {} y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \]

7784

\[ {} x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \]

7785

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

7786

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

7787

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

7788

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

7789

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

7790

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

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

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

7834

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

7835

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

7836

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

7837

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

7839

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

7840

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

7845

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

7863

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

7865

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

7980

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

7981

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

7985

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

7986

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

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

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

8006

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

8007

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

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

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

8014

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

8015

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