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# The general solution to the ODE is given. i) Verify that y solves the ODE. ii) Try to solve the initial value problem. ?

The general solution to the ODE is given.

i) Verify that y solves the ODE.

ii) Try to solve the initial value problem. Is there a unique solution, no solution, or infinitely

many solutions?

xy'' = y'; y(1) = -1; y'(1) = 2:

y = C1 + C2x^2

### 1 Answer

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- 1 month ago
y = C[1] + C[2] * x^2

y' = 0 + 2 * C[2] * x

y'' = 2 * C[2]

x * y'' = x * 2 * C[2] = 2 * C[2] * x = y'

Confirmed there

y'(1) = 2 * C[2] * 1 = 2 * C[2] = 2

C[2] = 1

y = C[1] + 1 * x^2

y = C[1] + x^2

y = -1 when x = 1

-1 = C[1] + 1

-2 = C[1]

y = x^2 - 2

y' = 2x

y'' = 2

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