Originally Posted by
kithy Help!!!
Find an implicit and an explicit solution of the given initial value problems.
a) dy/dt+2y=1, when y(0)=5/2
Mr F says: Many approaches are possible. Here are three:
1. Use the integrating factor method.
2. The DE is seperable: dt/dy = 1/(1 - 2y).
3. First order linear with constant coefficients. Assume a solution of the form y = $\displaystyle {\color{red}A e^{\lambda t} + B}$. Hint: B = 1/2, A is an arbitrary constant. Now find $\displaystyle {\color{red}\lambda}$.
b) (1+x^4)dy+x(1+4y^2)dx=0, when y(1)=0
Mr F says: The DE is seperable: $\displaystyle {\color{red}-\frac{dy}{1 + 4y^2} = \frac{x}{1 + x^4}}$. The y-integration is a standard form. For the x-integration, make the substitution u = x^2.
Thanks a lot!!!