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Popular >

16y^{''}+56y^'+49y=0,y(0)=5,y^'(0)=5

Solution

16 y^{^{''}} + 56 y^{^{'}} + 49 y = 0, y (0) = 5, y^{^{'}} (0) = 5

Solution

y = 5 e^{- \frac{7 t}{4}} + \frac{55 e ^{- \frac{7 t}{4}} t}{4}

Solution steps

16 y^{''} (t) + 56 y^{'} (t) + 49 y = 0

Solve linear ODE:

y = 5 e^{- \frac{7 t}{4}} + \frac{55 e ^{- \frac{7 t}{4}} t}{4}

y = 5 e^{- \frac{7 t}{4}} + \frac{55 e ^{- \frac{7 t}{4}} t}{4}

Graph

Popular Examples

100y^{''}+y=0,y(-10)=1,y^'(-10)=-1

100 y^{^{''}} + y = 0, y (- 10) = 1, y^{^{'}} (- 10) = - 1

y^{''}-3y^'+2y=0,y(0)=1,y^'(0)= 1/2

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{1}{2}

x^{''}+(sqrt(2))/(16)x^'+2x=0

x^{^{''}} + \frac{2}{16} x^{^{'}} + 2 x = 0

y^{''}-4y^'-5y=0,y(0)=2,y^'(0)=4

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 4

y^{''}+100y=0,y(0)=-2/3 ,y^'(0)=5

y^{^{''}} + 100 y = 0, y (0) = - \frac{2}{3}, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the solution for 16y^{''}+56y^'+49y=0,y(0)=5,y^'(0)=5 ?
The solution for 16y^{''}+56y^'+49y=0,y(0)=5,y^'(0)=5 is y=5e^{-(7t)/4}+(55e^{-(7t)/4}t)/(4)