8. What is the solution of the differential equation dy/dt = 4y^{2}t^{3}, subject to the condition y(1) = 1?
A. y = 1/(2-t^{4}) |
B. y = 2 – 1/t^{4} |
C. y = t^{4} |
D. y = 1/t^{4} |
E. y = e^(1-t^{2}) |
Solution: The answer is A
To solve for dy/dt separate the variables and the corresponding differentials as follows,
Integrating both sides of the above differential equation, yields,
Using the given initial condition we can solve for c, that is y(1)=1.
So, the solution of the differential equation is,