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Finding implicit form from differential equations

1. find the solution of the initial-value problem:

dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0

using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating.

2. a. find in implicit form, the general solution of the differential equation:

dy/dx = (4y^(1/2)(e^-x -e^x))/ ((e^x +e^-x)^2) (y>0)

b. find the corresponding explicit form of this general solution.

c. find the corresponding particular solution that satisfies the initial condition y=1 when x=0.

d. what is the value of y given by this particular solution when x=0.5 ? (give answer to 4 decimal places).

Solution Preview

finding implicit form from differential equations
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1. find the solution of the intitial-value problem:

dy/dx = (sin(3x))/(2+cos(3x)), y=4 when x=0

using equation: (f'(x))/(f(x)) dx = ln(f(x)) +c (f(x) > 0) when integrating.
Solution. Since dy/dx = (sin(3x))/(2+cos(3x)), we integrate it on both sides, ...

Solution Summary

This solution is comprised of a detailed explanation to find the solution of the initial-value problem.

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