Determine whether the differential equation is exact. If it is, then solve it. If it is not,...
Question:
Determine whether the differential equation is exact. If it is, then solve it. If it is not, solve it by first finding the appropriate integrating factor.
(a) {eq}\displaystyle (\sin y - y \sin x)\ dx + (\cos x + x \cos y - y)\ dy = 0 {/eq}.
(b) {eq}\displaystyle 4 x y\ dx + (4 y + 6 x^2)\ dy = 0 {/eq}.
Exact Differential Equation
An equation of the form M(x,y)dx+N(x,y)dy=0 is exact if
{eq}\frac{{\delta M}}{{\delta y}} = \frac{{\delta N}}{{\delta x}} {/eq}
Answer and Explanation: 1
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View this answera. (sin y-y sin x) dx+(cos x + x cos y-y ) dy=0
Here,
M(x,y)= siny - y sinx
and N(x,y)= cos x + x cos y -y
Now,
{eq}\eqalign{ & \frac{{\delta...
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Chapter 16 / Lesson 2The integrating factor method is useful in solving non-exact, linear, first-order, partial differential equations. Learn the technique of the integrating factors method and its application to the Fundamental Theorem of Calculus.