5. a) Show that the equation ydr +dy 0 is exact and solve it. b) In...
number 5 please
1-14 ODES. INTEGRATING FACTORS Test for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspection or by the theorems in the text. Also, if an initial condition is given, find the corresponding particular solution. 1. 2xy dx + x2 dy = 0 2. xºdx + y°dy = 0 3. sin x cos y dx + cos x sin y dy = 0 4. €3°(dr + 3r de) = 0 5....
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*...
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
Solve both 3+4 please
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
3. Solve the exact equation. Solve the Homogeneous equation 4. yar+(y-x)dy = 0.
In this question, we ask you to solve the differential equation dy (3x-6)2-(2y-s) dx satisfying the initial condition 4.1 (1 mark) Hopefully, you have observed that the d.e. is separable. Thus, as a first step you need to rearrange the d.c. in the form for appropriate functions fy) and g(x) Enter such an equation, below y) dy-g(x) dx Note. The differentials dx and dy are simply entered as dx and dy, respectively separated d.e You have not attempted this yet...
1. Find the particular solution of the differential
equation
dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x)
satisfying the initial condition y(0)=4y(0)=4.
2. Solve the following initial value problem:
8dydt+y=32t8dydt+y=32t
with y(0)=6.y(0)=6.
(1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...
Determine whether the equation is exact. If it is, then solve it (3x2y+8)dx+ (x3-8)dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A The equation is exact and an implicit solution in the form F(x.y) = C is _______ = C, where C is an arbitrary constant. B. The equation is not exact.
4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0
4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0
Determine whether the equation is exact. If it is, then solve it. (3x²y+9) dx + (x3 - 6) dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = A. The equation is exact and an implicit solution in the form F(x,y) = C is _______ = C, where is an arbitrary constant.(Type an expression using x and y as the variables.) B. The equation is not exact.
1) Consider the following equation. 6xy dx (4y 9x2)dy-0 a) Show the equation is not exact. b) Find an integrating factor that will make it exact. c) Use the integrating factor to solve the resulting exact equation.