Solve the given linear differential equation subject to the indicated initial condition. dy 1 -y= xe*...
(1 point) Solve the separable differential equation dy da: 2 Subject to the initial condition: y(0) 8.
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
Find a function y=f(x) satisfying the given differential equation and the prescribed initial condition. 1 dy dx y(7) = -5 1x + 2
Solve the following equation with given initial condition: dy dx = xcos² y, y(0) = 0.
Find the solution of the differential equation with the given initial condition. Dy/dx = 2x + sec^2x/2y, y(0) = 5.
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form. 5. Find the solution of the differential equation that satisfies the given initial condition dy cos' xsin dx ysin y Yo) - 1. Leave the answer in the implici form. ,y(o)- 1. Leave the answer in the implicit form.
(1 point) Solve the separable differential equation dx Subject to the initial condition: y(0)-7. sqrt(11/4(sqrt(xA2+1))+47/4)
No 4. Solve the differential equation dy dx . Solve the initial value problem: y" + 3y' + 2y 10 cosx, y(0) 1,y'(0) 0
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*...