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Popular >

y^{''}+3y^'+1=0

Solution

y^{^{''}} + 3 y^{^{'}} + 1 = 0

Solution

y = c_{1} + c_{2} e^{- 3 t} - \frac{t}{3}

Solution steps

y^{''} (t) + 3 y^{'} (t) + 1 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 3 t} - \frac{t}{3}

y = c_{1} + c_{2} e^{- 3 t} - \frac{t}{3}

Graph

Popular Examples

4y^{''}-y=(ex)/(2+4)

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

y^{''}-10y^'+25y=((e^{-5x})/(1+x^2))

y^{^{''}} - 10 y^{^{'}} + 25 y = (\frac{e ^{- 5 x}}{1 + x ^{2}})

x^{''}-12x^'+36x=2t+e^{6t}

x^{^{''}} - 12 x^{^{'}} + 36 x = 2 t + e^{6 t}

y^{''}+y=-3,y(0)=0,y^'(0)=1

y^{^{''}} + y = - 3, y (0) = 0, y^{^{'}} (0) = 1

4y^{''}-y=(ex)/(2+5)

4 y^{^{''}} - y = \frac{e x}{2 + 5}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'+1=0 ?
The solution for y^{''}+3y^'+1=0 is y=c_{1}+c_{2}e^{-3t}-t/3