(4) Solve each first order separable equation. (a) V (b) sin22:dy = sec2u dy Vry =sec"...
Solve the separable differential equation (y2+2)dx+y(x+4)dy=0.
Solve the Separable Differential Equation. dy 1) e6x - 6y dx A) y = 6ln (e6x + C) B) y = 6e6x + C y-In (ex.c) D) y = ln (e6x + C) = 4 cos x sec y A) y = sin (4 sin x + C) C) y=sin-1 (4 cos x + C) B) y = sin-1 (4 sin x + C) D) y = 4 sin x + C
QUESTION 11 +3x Solve the first-order differential equation dy e2y2 = dx у
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
ether they are on you will receive an Ffo 1. Solve the first-order differential equation dy - x2+xy+ya with y(-1) = 1. (10pts) dx 2. Solve the initial value problem dy + y cot x = y sin x, with y(1/2) = 1. (10pts) dx 3. Given the system of linear coun X2
5. Solve the first order differential equation. my dy - z3 cos y dx = 0 sin :
dy 4. (a) Classify the following differential equation: +yrsin(a) i. ORDER ii. LINEAR/NONLINEAR: iii. SEPARABLE/NOT SEPARABLE: (b) Use your classification from (a) to use an appropriate method in the following problem. Be sure to clearly label steps to maximize your score Find an explicit solution of +y=sin(x). Explicit Solution: (c) Give the largest interval over which the general solution is defined. (d) Are there any transient terms in the general solution? If yes, what are they?
ho Question 1 Solve the separable DE. dy zy dx = dạy2 + x2 + 3y2 +3 »(+4) *+1) = 20+C y2 +1 In = 26 +0 y? + In 26 In (*+1) ==+0
Question 14 (12 marks) Consider the following separable differential equation. dy cos(z)(-1) dr (a) Find any constant solutions of this differential equation and hence write down the solution with initial value y=- when r=7 (b) Use partial fractions to evaluate 1 dy. 1 (c) Use the method for solving separable differential equations to solve this DE in the case where y 0 when r T. You may assume that the solution does not cross the constant solutions you found in...
(1 point) Solve the separable differential equation dy da: 2 Subject to the initial condition: y(0) 8.