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Popular >

y^{''}+y^'-12y=e^x+e^{2x}-1

Solution

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

Solution

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

Solution steps

y^{''} (x) + y^{'} (x) - 12 y = e^{x} + e^{2 x} - 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

Graph

Popular Examples

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

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

y^{''}-y^'=e^{2x},y(0)=0,y(1)=0

y^{^{''}} - y^{^{'}} = e^{2 x}, y (0) = 0, y (1) = 0

x^{''}+4x=cos(2t)

x^{^{''}} + 4 x = cos (2 t)

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

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

y^{''}+4y=-5,y(pi/8)=-1/4 ,y^'(pi/8)=2

y^{^{''}} + 4 y = - 5, y (\frac{π}{8}) = - \frac{1}{4}, y^{^{'}} (\frac{π}{8}) = 2

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'-12y=e^x+e^{2x}-1 ?
The solution for y^{''}+y^'-12y=e^x+e^{2x}-1 is y=c_{1}e^{3x}+c_{2}e^{-4x}-1/10 e^x-1/6 e^{2x}+1/12