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Popular >

y^{''}-(4y^')/3+(97y)/(36)=0

Solution

y^{^{''}} - \frac{4 y ^{^{'}}}{3} + \frac{97 y}{36} = 0

Solution

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Solution steps

y^{''} (t) - \frac{4 y ^{'} ( t )}{3} + \frac{97 y}{36} = 0

Solve linear ODE:

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

y = e^{\frac{2 t}{3}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2}))

Graph

Popular Examples

y^{''}-10y^'+25y=0,y(0)=3,y^'(0)= 31/2

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = \frac{31}{2}

4(dy)/(dx)-3(d^2y)/(dx^2)=0

4 \frac{d y}{d x} - 3 \frac{d ^{2} y}{d x ^{2}} = 0

y^{'''}+5y^{''}-11y^'-39y=0

y^{^{'''}} + 5 y^{^{''}} - 11 y^{^{'}} - 39 y = 0

4y^{''}+12y^'+9y=0,y(0)=3,y^'(0)=5

4 y^{^{''}} + 12 y^{^{'}} + 9 y = 0, y (0) = 3, y^{^{'}} (0) = 5

y^{''''}+5y^{''}-36y=0

y^{^{''''}} + 5 y^{^{''}} - 36 y = 0

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-(4y^')/3+(97y)/(36)=0 ?
The solution for y^{''}-(4y^')/3+(97y)/(36)=0 is y=e^{(2t)/3}(c_{1}cos((3t)/2)+c_{2}sin((3t)/2))