Find the specific solution for the following differential equations:

a) (dy/dx)^2 - x^4 = 0 given the initial value y(1) = 0

b) dy/dx = ysinx given the initial value y(pi) = 1

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- Nov 10th 2008, 10:23 AMPurplePenguinSolving differential equations
Find the specific solution for the following differential equations:

a) (dy/dx)^2 - x^4 = 0 given the initial value y(1) = 0

b) dy/dx = ysinx given the initial value y(pi) = 1 - Nov 10th 2008, 10:36 AMChris L T521
Rearrange to get $\displaystyle \frac{\,dy}{\,dx}=x^2$

This should be easy enough to solve now...

Quote:

b) dy/dx = ysinx given the initial value y(pi) = 1

Now integrate both sides and then solve for y.

In both of these, apply the initial condition after you have integrated and solved for y. This will help you determine the value of the arbitrary constant $\displaystyle C$.

--Chris