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

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Problem: Differential equation: $y^{\prime }=xy$ 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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