What is the solution for y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2 ?

The solution for y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2 is y=e^{3t}(3cos(t)-11sin(t))

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y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2

y^{^{''}} - 6 y^{^{'}} + 10 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

y = e^{3 t} (3 cos (t) - 11 sin (t))

Solution steps

y^{''} (t) - 6 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = e^{3 t} (3 cos (t) - 11 sin (t))

y = e^{3 t} (3 cos (t) - 11 sin (t))

7 x^{2} + 4 x - 5

\int - 5 x cos (x) d x

\frac{d}{d x} ((y - x)^{2})

x \to 2 lim (∣ x - 3 ∣)

What is the solution for y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2 ?
The solution for y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2 is y=e^{3t}(3cos(t)-11sin(t))