Solve the differential equation to y +y= V1+ cos2 z, y(1) = 4. Then y =...
Solve the differential equation to y' +y= V1 + cos2 x, y(1) = 4. Then y= ___ when x = 2.
Question 4 Solve the differential equation. 2xy' + y = 2V* Question 5 Solve the initial value problem xy' + y = xln x , y(1) = 0 Question 7 Find the derivative. c = tet, g =t+ sin t Question 8 Find the equation of the tangent to the curve at the given point. x = ť – t, y=ť +t+1 ; (0,3)
Solve the differential equation given the initial condition provided. Do not solve explicity for y. = xy? – xy” cos x, y(0) = 1
#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
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
1. Solve differential equation by variation of parameters 4y" – 4y' + y = ež V1 – 12 2. Solve differential equation by variation of parameters 2x y" – 34" + 2y = 1+ er
Solve the following differential equation y(z) – 2 (dy (z)) – 15 y (z) = 0, with y(0) = 1, y'(0) = -27 d22 Enter your answer in Maple syntax in the format "y(x)= ...." For example, if your answer is y(t) = 3e-+421, enter y(x)=3*exp(-x)+4*exp(2*x) in the box.
exact differential equations 2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
Please show all the steps of these questions. Solve the differential equation y' + y cos x = { sin 2x dy V1 - y2 Solve the initial value problem y(e) = dx x In (x) 1 = V2
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