(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve [tex] \frac{d^2 y}{dt^2} = y [/tex]

2. Relevant equations

3. The attempt at a solution

[tex] \frac{dy}{dt} = v [/tex]

[tex] \frac{d^2 y}{dt^2} = v \frac{dv}{dy} [/tex]

[tex] v \frac{dv}{dy} = y [/tex]

[tex] v dv = y dy [/tex]

[tex] \int v dv = \int y dy [/tex]

[tex] v^2 = y^2 + C [/tex]

[tex] ( \frac{dy}{dt} )^2 = y^2 + C [/tex]

[tex] \frac{dy}{dt} = \sqrt{ y^2 + C } [/tex]

[tex] \int \frac{dy}{ \sqrt{ y^2 + C }} = \int dt [/tex]

[tex] \int \frac{dy}{ \sqrt{ y^2 + C }} = t [/tex]

I have no idea how to integrate this. Have I gone wrong somewhere?

Thanks in advance for any help.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Differential equations

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