What is the solution for y^{''}+pi^2y=0,y(0)=1,y^'(0)=1 ?

The solution for y^{''}+pi^2y=0,y(0)=1,y^'(0)=1 is y=cos(pit)+1/pi sin(pit)

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y^{''}+pi^2y=0,y(0)=1,y^'(0)=1

y^{^{''}} + π^{2} y = 0, y (0) = 1, y^{^{'}} (0) = 1

y = cos (π t) + \frac{1}{π} sin (π t)

Solution steps

y^{''} (t) + π^{2} y = 0

Solve linear ODE:

y = cos (π t) + \frac{1}{π} sin (π t)

y = cos (π t) + \frac{1}{π} sin (π t)

4 y^{^{''}} - 36 y = 0

x^{^{''}} + 2 x^{^{'}} + (1 - k) x = 0

49 y^{^{''}} + 36 y = 0

100 y^{^{''}} + 60 y^{^{'}} + 90 y = 0, y (1) = 9, y^{^{'}} (1) = 2

x^{^{'''}} + 9 \cdot x^{^{''}} + x^{^{'}} + 9 x = 0

What is the solution for y^{''}+pi^2y=0,y(0)=1,y^'(0)=1 ?
The solution for y^{''}+pi^2y=0,y(0)=1,y^'(0)=1 is y=cos(pit)+1/pi sin(pit)