Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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 infi nitely

many solutions?

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

y = C1 + C2x^2

1 Answer

Relevance
  • 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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