What is the solution for y^{''}+y=2,y(0)=2,y^'(0)=3 ?

The solution for y^{''}+y=2,y(0)=2,y^'(0)=3 is y=3sin(t)+2

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

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

y = 3 sin (t) + 2

Solution steps

y^{''} (t) + y = 2

Solve linear ODE:

y = 3 sin (t) + 2

y = 3 sin (t) + 2

y^{^{''}} - y = \frac{4 e ^{- x}}{1 - e ^{- 2 x}}

y^{^{''}} - 2 y^{^{'}} + y = x^{\frac{1}{3}} e^{x}

y^{^{'''}} + y^{^{'}} = e^{x}

y^{^{''}} + 4 y = 4 t, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 4 y = 9 t

What is the solution for y^{''}+y=2,y(0)=2,y^'(0)=3 ?
The solution for y^{''}+y=2,y(0)=2,y^'(0)=3 is y=3sin(t)+2