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Popular >

y^{''}+k^2*y=0

Solution

y^{^{''}} + k^{2} \cdot y = 0

Solution

y = c_{1} cos (k t) + c_{2} sin (k t)

Solution steps

y^{''} (t) + k^{2} \cdot y = 0

Solve linear ODE:

y = c_{1} cos (k t) + c_{2} sin (k t)

y = c_{1} cos (k t) + c_{2} sin (k t)

Graph

Popular Examples

linear y^{''}=y linear

y^{^{''}} = y

y^{''}-7y^'-8y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 7 y^{^{'}} - 8 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

y^{''''}-8y^{'''}+18y^{''}-27y=0

y^{^{''''}} - 8 y^{^{'''}} + 18 y^{^{''}} - 27 y = 0

y^{''}+y^'=0,y^'(0)=1

y^{^{''}} + y^{^{'}} = 0, y^{^{'}} (0) = 1

3y^{''}+2y^'=0,y(0)=-6,y^'(0)=-18

3 y^{^{''}} + 2 y^{^{'}} = 0, y (0) = - 6, y^{^{'}} (0) = - 18

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+k^2*y=0 ?
The solution for y^{''}+k^2*y=0 is y=c_{1}cos(kt)+c_{2}sin(kt)