Determine whether the given differential equation is exact. If it is exact, solve it. If not,...
Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (1 + ln(x) + y/x) dx = (2− ln(x))
1: Determine whether the given differential equation is exact Q1: Determine whether the given differential equation is exact a) [1 + In(xy)]dx + (dy = 0 소 소 전 소 소 be xydx - (xy2 + y3)dy = 0 t
(2) (13 points) Determine whether the given differential equation s e If it is exact, solve it:
[8] 2. Consider the differential equation dx + (1 - sin(v)) dy = 0 Determine if the equation is exact. If so, solve. If not determine an approximation integrating acco the equation exact. Verify that the new equation is exact, and solve the differential equation using the integrating factor you have found. (Hint: the integrating factor should be a function of y only.)
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
#4 Solve the following: (1 point) Solve the differential equation 6y 2 +2 where y 6 when 0 (1 point) The differential equation can be written in differential form: M(x, y) dz +N(z, ) dy-0 where ,and N(x, y)--y5-3x The term M(, y) dz + N(x, y) dy becomes an exact differential if the left hand side above is divided by y4. Integrating that new equation, the solution of the differential equation is E C
2. Determine whether the given equation is exact. If it is solve the equation a)y" +xy'-y=0 b) xy" - (cosx)y' + (sin)y = 0, y>0c) x2 + xy' - y, x > 0
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
The equation$$ \left(3 y e^{x}-2\right) d x+\left(e^{x}\left(3 x+4 y^{3}\right)\right) d y=0 $$in differential form \(\widetilde{M} d x+\widetilde{N} d y=0\) is not exact. Indeed, we have$$ \bar{M}_{y}-\widetilde{N}_{x}= $$For this exercise we can find an integrating factor which is a function of \(x\) alone since$$ \frac{\bar{M}_{y}-\bar{N}_{x}}{\bar{N}}= $$can be considered as a function of \(x\) alone.Namely we have \(\mu(x)\)Multiplying the original equation by the integrating factor we obtain a new equation \(M d x+N d y=0\) where$$ M= $$$$ N= $$Which is exact...
In this problem we consider an equation in differential form M dx + N dy = 0. The equation (2е' — (16х° уе* + 4e * sin(x))) dx + (2eY — 16х*y'е*)dy 3D 0 in differential form M dx + N dy = 0 is not exact. Indeed, we have For this exercise we can find an integrating factor which is a function of x alone since м.- N. N can be considered as a function of x alone. Namely...