4.3.29 Problems 2801 to 2900

Table 4.421: Second order ode

#

ODE

Mathematica

Maple

Sympy

9656

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

9657

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

9658

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

9659

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \]

9660

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

9661

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]

9662

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

9663

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

9664

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \]

9775

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

9776

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

9777

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

9778

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

9779

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

9780

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

9781

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

9782

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

9783

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

9784

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

9785

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

9786

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

9787

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

9788

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

9789

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

9790

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

9791

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

9792

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

9793

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

9794

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

9795

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

9796

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

9797

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

9798

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

9799

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

9800

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

9801

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

9802

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

9803

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

9804

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

9805

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

9806

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

9807

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

9808

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

9809

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

9810

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

9811

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

9812

\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]

9813

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

9814

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

9815

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

9816

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

9817

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

9818

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

9892

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

9893

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

9894

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

9895

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

9896

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

9897

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

9898

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

9899

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

9900

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

9912

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

9943

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

9991

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

9992

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

9993

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

9994

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

10038

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

10039

\[ {} 5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]

10040

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

10041

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

10045

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

10046

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

10047

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

10048

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

10049

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

10050

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

10051

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

10052

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

10053

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

10054

\[ {} y^{\prime \prime } = f \left (t \right ) \]

10055

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

10058

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

10059

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

10060

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

10061

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

10062

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

10063

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

10064

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

10065

\[ {} 3 y y^{\prime \prime }+y = 5 \]

10066

\[ {} a y y^{\prime \prime }+b y = c \]

10067

\[ {} a y^{2} y^{\prime \prime }+b y^{2} = c \]

10068

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10085

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

10086

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

10087

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

10088

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

10089

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