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Popular >

y^{''}+4y=1

Solution

y^{^{''}} + 4 y = 1

Solution

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{1}{4}

Graph

Popular Examples

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

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

y^{''}+3y^'+2y= 1/(1+e^{2x)}

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

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

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

2y^{''}=-2y+2cos^2(x)

2 y^{^{''}} = - 2 y + 2 cos^{2} (x)

6y^{''}-13y^'-5y=5x^3+39x^2-36x-10

6 y^{^{''}} - 13 y^{^{'}} - 5 y = 5 x^{3} + 39 x^{2} - 36 x - 10

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+4y=1 ?
The solution for y^{''}+4y=1 is y=c_{1}cos(2t)+c_{2}sin(2t)+1/4