Dx+Dy = e b. -D r + Dx + I + y = 0 C Dx+Dy = e b. -D r + Dx + I + y = 0 C
x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a) x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a)
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
explain please 2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e + y)<x+ſe+x)dy = 0 c.(ye* +1) dx +(e' + xy) dy = 0 d. (sin x+cos y) dx +(cos x +sin y) dy = 0 e. (eº+1) dx +(e? + 2) dy = 0 3. The solution of the following separable DE xy' =-y? is a. y= '+c b. y=- c. y = In x+c In x+c d. In y=x? + e. yer+C 4....
(a) [1[*(2x*y + 4y2) dy dx (b) ["" ["(y cos(x) + 6) dy dx cos [**(buye* * *) ay ox (a) LiS.*r-* log(4) dy dx (-x log(y)) dy dx -Il
Q1: Solve the ODE: f) Vyy' + y3/2-1. y(1) = 0. g) (2x +y)dx(2x+y-1)dy 0. i) dx=xy2e": y(2)=0. j) (1 + x*)dy + (1 + y*)dx = 0; y(1) = V3. Q1: Solve the ODE: f) Vyy' + y3/2-1. y(1) = 0. g) (2x +y)dx(2x+y-1)dy 0. i) dx=xy2e": y(2)=0. j) (1 + x*)dy + (1 + y*)dx = 0; y(1) = V3.
solve the following differential equations (e* + 2y)dx + (2x – sin y)dy = 0 xy' + y = y? (6xy + cos2x)dx +(9x?y? +e")dy = 0 +2ye * )dx = (w*e * -2rcos x) di
Evaluate I=∫C(sinx+9y)dx+(8x+y)dy for the nonclosed path ABCD in the figure. A=(0,0),B=(4,4),C=(4,8),D=(0,12) (1 point) Evaluate I figure. Je(sin x +9y) dx + (8x + y) dy for the nonclosed path ABCD in the A (0,0), B (4,4, C (4,8), D (0,12)
Solve e^x dy/dx = x sec (y) y (0) = pi
The solution of the IVP dy dx = (ax+by+1)2 – 6; y(0)=0, where a € R and b ERVO} Select one: a. (ax +by+1)(1+x)= 1 O b. (ax+by+1)(1-x)=3 O c. (ax+by+1)2(1 - bx)=1 2 O d. (ax +by+1)= 1- bx e. (ax+by+1)(1-bx)= 1 of. (ax +by+1) (1 -bx)2 = 1 о g. (ax +by-1)(1-bx) = 1 O h. ax + by=1
a) dy de d b) de dy dx a) dy de d b) de dy dx