Boundary Value Problems/Introduction to BVPs/IVP-student-1

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Problem: Differential equation: $$y'=xy$$ with initial condition: $$y(0)=3 $$

Start Solution:

$$\int \frac{1}{y}dy = \int x dx $$

$$ln(|y|) = \frac{x^2}{2} +C $$

$$ e^{ln(|y|)} = e^{\frac{x^2}{2} +C} $$

$$ |y| = e^{\frac{x^2}{2}}e^C $$

$$ |y| = e^{\frac{x^2}{2}} C_1 $$

$$ |y| = C_1 e^{\frac{x^2}{2}} $$

Use the initial condition $$ y(0)= 3 $$ to solve for the constant $$ C_1 $$.

$$ |y(0)| = 3 = C_1 e^0 $$

$$ C_1 =3 $$

The particular solution to the initial value problem is:

$$ y = 3 e^{\frac{x^2}{2}} $$ /Why did I drop the "absolute value" operation/?

End Solution:

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