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:

$\int {\frac {1}{y}}dy=\int xdx$

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

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

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

$|y|=e^{\frac {x^{2}}{2}}C_{1}$

$|y|=C_{1}e^{\frac {x^{2}}{2}}$

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:

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

End Solution:

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