I need help with problem 4 solving the exact differential equation and finding the integrating factor.
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PROBLEMS (Exact Equations).
Find the value of b such that the following equations are exact and then find their
1
general solution.
(a) (xy² + bx²y) + (x + y)x²y' = 0,
(b) (ye2y + x) + bxe²yy' = 0.
2: Find the general solution to the following differential equations.
(a) (e* sin(y) - 2ysin(x)) + (ecos (y) +2cos(x)) y' = 0,
(b) (2xy² + 2y) + (2xy + 2x)y' = 0,
Y
(c) ( + 6x) + (ln(x) — 2)y' = 0,
-
(d) (xln(y) + xy) + (yln(x) + xy)y' = 0,
(e) (2x + 2y) + (2x - 2y)y' = 0.
3: Solve the following first order differential equations by first finding the integrating
factor.
1
(1) (2xy² + y) + (2y³ − x)y' = 0
(2) (2x+tan y) + (x-r²tan y)y' = 0
(3) x²y³ + x1 + y²)y' = 0
(4) (siny - 2e-sinx) + (cosy+2e) y' = 0
Cos/x)
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Expert Solution
Step 1
The given differential equation is
.
We have to solve the differential equation and also find the integrating factor.
