What is the solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 ?

The solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 is y=(1+15/4)e^{(3t)/2}-15/4 e^{-t/2}

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4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 9

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

Solution steps

4 y^{''} (t) - 4 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

y = (1 + \frac{15}{4}) e^{\frac{3 t}{2}} - \frac{15}{4} e^{- \frac{t}{2}}

x \to - π lim (csc (x))

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{6})

\int \frac{1 - x ^{2}}{( x ^{2} - 1 ) ^{2}} d x

x \to 2 lim (x^{2} - 3 x)

y^{^{''}} + 2 y^{^{'}} = 2 x + 7 - e - 2 x

What is the solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 ?
The solution for 4y^{''}-4y^'-3y=0,y(0)=1,y^'(0)=9 is y=(1+15/4)e^{(3t)/2}-15/4 e^{-t/2}