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Popular >

3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x}

Solution

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

Solution

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

Solution steps

3 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 4 y = 10 e^{- 3 x}

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}+7y^'+6y=8

y^{^{''}} + 7 y^{^{'}} + 6 y = 8

y^{''}+4y=3sin(t),y(0)=2,y^'(0)=-1

y^{^{''}} + 4 y = 3 sin (t), y (0) = 2, y^{^{'}} (0) = - 1

y^{''}-4y=3e^{2x},y(0)=0,y^'(0)=0

y^{^{''}} - 4 y = 3 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

2y^{''}+3y^'-2y=te^{-2t}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = t e^{- 2 t}

x^{''}+0.8x^'+19.6x=4e^{-2t}cos(6t)

x^{^{''}} + 0.8 x^{^{'}} + 19.6 x = 4 e^{- 2 t} cos (6 t)

Frequently Asked Questions (FAQ)

What is the solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} ?
The solution for 3(d^2y)/(dx^2)+(dy)/(dx)-4y=10e^{-3x} is y=c_{1}e^x+c_{2}e^{-(4x)/3}+1/2 e^{-3x}