What is the solution for y^{''}+y=0,y^'(pi/4)=sqrt(2),y^'(0)=1 ?

The solution for y^{''}+y=0,y^'(pi/4)=sqrt(2),y^'(0)=1 is y=-cos(t)+sin(t)

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y^{''}+y=0,y^'(pi/4)=sqrt(2),y^'(0)=1

y^{^{''}} + y = 0, y^{^{'}} (\frac{π}{4}) = 2, y^{^{'}} (0) = 1

y = - cos (t) + sin (t)

Solution steps

y^{''} (t) + y = 0

Solve linear ODE:

y = - cos (t) + sin (t)

y = - cos (t) + sin (t)

y^{^{''}} + 0 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 15 y = 0, y (0) = 1

5 y^{^{''}} + 20 y = 0, y (\frac{π}{4}) = 10, y (0) = 15

2 y^{^{''}} + 6 y^{^{'}} = 0

y^{^{''}} + c^{2} y = 0, y (0) = a, y^{^{'}} (0) = 0

What is the solution for y^{''}+y=0,y^'(pi/4)=sqrt(2),y^'(0)=1 ?
The solution for y^{''}+y=0,y^'(pi/4)=sqrt(2),y^'(0)=1 is y=-cos(t)+sin(t)