Verify that the given functions y 1 and y 2 are linearly independent solutions of the following differential equation and find the solution that satisfies the given initial conditions. t y ′′ − ( t + 2 ) y ′ + 2 y = 0 ; y 1 ( t ) = e t , y 2 ( t ) = t 2 + 2 t + 2 ; y ( 1 ) = 0 , y ′ ( 1 ) = 1
Verify that the given functions y 1 and y 2 are linearly independent solutions of the following differential equation and find the solution that satisfies the given initial conditions. t y ′′ − ( t + 2 ) y ′ + 2 y = 0 ; y 1 ( t ) = e t , y 2 ( t ) = t 2 + 2 t + 2 ; y ( 1 ) = 0 , y ′ ( 1 ) = 1
Solution Summary: The author explains that the given functions are linearly independent solutions of the following differential equation and find the solution that satisfies the initial conditions.
Verify that the given functions
y
1
and
y
2
are linearly independent solutions of the following differential equation and find the solution that satisfies the given initial conditions.
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