CPM Homework Help : APCALC Problem 9-121

Solve the differential equation $\frac { d y } { d x } = (1 + y^2)e^{2x}$ if $(0, 1)$ lies on the solution curve.

Step 1:

$\frac{dy}{1+y^2}=e^{2x}dx$

Step 2:

$\int\frac{dy}{1+y^2}=\int e^{2x}dx$

Step 3:

$\tan^{-1}(y)=\frac{1}{2}e^{2x}+C$

Step 4:

Use the point $(0, 1)$ to solve for $C$ .