What is the solution for y^{''}-10y^'+41y=0,y(0)=10,y^'(0)=7 ?

The solution for y^{''}-10y^'+41y=0,y(0)=10,y^'(0)=7 is y=e^{5t}(10cos(4t)-43/4 sin(4t))

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y^{''}-10y^'+41y=0,y(0)=10,y^'(0)=7

y^{^{''}} - 10 y^{^{'}} + 41 y = 0, y (0) = 10, y^{^{'}} (0) = 7

y = e^{5 t} (10 cos (4 t) - \frac{43}{4} sin (4 t))

Solution steps

y^{''} (t) - 10 y^{'} (t) + 41 y = 0

Solve linear ODE:

y = e^{5 t} (10 cos (4 t) - \frac{43}{4} sin (4 t))

y = e^{5 t} (10 cos (4 t) - \frac{43}{4} sin (4 t))

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 10 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 5, y^{^{'}} (0) = 26

(d^{5} - 6 d^{4} + 9 d^{3}) y = 0

What is the solution for y^{''}-10y^'+41y=0,y(0)=10,y^'(0)=7 ?
The solution for y^{''}-10y^'+41y=0,y(0)=10,y^'(0)=7 is y=e^{5t}(10cos(4t)-43/4 sin(4t))