AP Calculus AB / Unit 7: Differential Equations
7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
Notes
After separating and integrating, use the initial condition to find $C$, then solve for $y$.
Practice
Solve $\displaystyle \frac{dy}{dx}=2x$, $y(1)=4$.
$4=1+C$.
Solve $\displaystyle \frac{dy}{dx}=y$, $y(0)=3$.
$y=Ce^x$, $C=3$.
Solve $\displaystyle \frac{dy}{dx}=\frac{x}{y}$, $y(0)=2$.
$y^2=x^2+4$; take the positive root since $y(0)=2>0$.
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