1. ## Initial value Problem

Help!!!

Find an implicit and an explicit solution of the given initial value problems.
a) dy/dt+2y=1, when y(0)=5/2

b) (1+x^4)dy+x(1+4y^2)dx=0, when y(1)=0

Thanks a lot!!!

2. 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 = ${\color{red}A e^{\lambda t} + B}$. Hint: B = 1/2, A is an arbitrary constant. Now find ${\color{red}\lambda}$.

b) (1+x^4)dy+x(1+4y^2)dx=0, when y(1)=0

Mr F says: The DE is seperable: ${\color{red}-\frac{dy}{1 + 4y^2} = \frac{x}{1 + x^4}}$. The y-integration is a standard form. For the x-integration, make the substitution u = x^2.

Thanks a lot!!!
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