What is the solution for 4y^{''}-12y^'+9y=0,y(0)=3,y^'(0)=5 ?

The solution for 4y^{''}-12y^'+9y=0,y(0)=3,y^'(0)=5 is y=3e^{(3t)/2}+(e^{(3t)/2}t)/(2)

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

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

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

Solution steps

4 y^{''} (t) - 12 y^{'} (t) + 9 y = 0

Solve linear ODE:

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

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

n \to \infty lim (\frac{ln ( n )}{ln ( 2 n )})

\int \frac{1}{( x - 3 ) ( x + 4 )} d x

x \to 0 lim (x^{0})

f (x) = \frac{1}{x - 3}

\int (e^{2 x})^{2} d x

What is the solution for 4y^{''}-12y^'+9y=0,y(0)=3,y^'(0)=5 ?
The solution for 4y^{''}-12y^'+9y=0,y(0)=3,y^'(0)=5 is y=3e^{(3t)/2}+(e^{(3t)/2}t)/(2)