Daniela tried to solve the differential equation dy d: 9 = 22.e-y. This is her work:...
Show that the function y = cos (ln(x)] satisfies the differential equation 22 day dy +2 dx +y = 0. dc2
Use the change of variables to solve the differential equation. 5. xy' = y +2Vxy dy Y-3 dx y + x 7. cy' + y ln x = y lny 8. (x + yey/t) dx – xey/dy = 0, y(1) = 0)
Need number 22. Please explain. In Problems 19–26 solve the given differential equation. 19. (y2 + 1) dx = y sec? x dy 20. y(In x – In y) dx = (x In x - x ln y - y) dy dy 21. (6r: + 1)y? + 3x² + 2y3 = 0 dx dx 22. dy 4y2 + 6xy 3y2 + 2x
Solve the differential equation. dy dx 3.c2e- y=In(x3 + C) y=Cln(x) y=+*+ Oy=ln(3x + C)
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*...
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
solve for the given differential equation dy 8. dx x y In each of Problems 9 through 16.
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
Solve the given differential equation. 9) dy + y = 14 +6 cos 3x 9) dx² B) y = ci sin x + c2 cos A) y=cı sin x +c2 cos x + cos 3x +14 C)y=cı sin x +c2 cos x - cos 3x +14 D) y=q sin x +02 cos x - sin 3x+14
Solve differential equation. (x/y) (dx/dy) +(ln(y) - x) =0 I have been told it is not solved by substitution. It doesn't look exact or separable. It appears to be linear, but the mixed variable for qx and the natural log is confusing to me.