4.3.77 Problems 7601 to 7700

Table 4.517: Second order ode

#

ODE

Mathematica

Maple

Sympy

21643

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

21644

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

21645

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \]

21646

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

21647

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 2 x -40 \cos \left (2 x \right ) \]

21648

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \]

21655

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

21656

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

21657

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

21658

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

21659

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

21660

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

21661

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

21662

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

21663

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

21664

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

21665

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

21669

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

21670

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

21671

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

21672

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

21673

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

21675

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

21676

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

21679

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

21680

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

21681

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

21682

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

21683

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

21684

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

21685

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

21687

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

21688

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

21691

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 16 x^{3} {\mathrm e}^{3 x} \]

21693

\[ {} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}+7 x -2 \]

21695

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

21696

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

21697

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

21700

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

21701

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

21702

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

21704

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

21707

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

21715

\[ {} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0 \]

21716

\[ {} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y = x^{3}-3 x^{2}+3 x -8 \]

21717

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

21718

\[ {} x^{2} u^{\prime \prime }-3 u^{\prime } x +13 u = 0 \]

21720

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

21721

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

21725

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

21727

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

21728

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

21729

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

21730

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 1 \]

21731

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

21732

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

21733

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

21734

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

21735

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

21736

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

21737

\[ {} \theta ^{\prime \prime }+4 \theta = 15 \cos \left (3 t \right ) \]

21740

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

21828

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

21829

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

21830

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

21831

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

21832

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

21833

\[ {} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right . \]

21834

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \]

21835

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right . \]

21836

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

21842

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

21843

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

21844

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

21845

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

21846

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

21850

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

21873

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

21874

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

21875

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

21876

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

21877

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

21878

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

21879

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

21880

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

21881

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

21903

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

21904

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

21905

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

21908

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

21909

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

21990

\[ {} y^{\prime \prime }-12 y^{\prime }+35 y = 0 \]

21991

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

21992

\[ {} 9 y^{\prime \prime }-30 y^{\prime }+25 y = 0 \]

21993

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

21999

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

22000

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

22001

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

22002

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

22003

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