# Separating variables and integrating leads you to

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Separating variables and integrating leads you to . After doing that and completing the integration, you’ll obtain or an equivalent beast. You may then finish this by replacing v above with y / x . Additional algebra will lead to the same 1-parameter family of implicit solutions as the exact route.

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TEST1/MAP2302 Page 3 of 3 ______________________________________________________________________ 2. (6 pts.) What conditions on the coefficients of the following homogeneous equation are sufficient for the equation to be exact? Do not attempt to solve the DE. Since and , and polynomials of two variables have continuous second order partial derivatives on the whole of the xy-plane, the equation will be exact precisely when ______________________________________________________________________ 3. (6 pts.) Every solution to the differential equation y - 16 y = 0 is of the form . Which of these functions satisfies the initial conditions y (0) = 4 and y (0) = 8 ?? The initial conditions lead to the system of equations which is equivalent to The solution to the IVP is given by . ______________________________________________________________________ 4. (8 points) The following differential equation may be solved by either performing a substitution to reduce it to a separable equation or by performing a different substitution to reduce it to a homogeneous equation.
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