1) Write a differential equation describing this system. This means find the equation of the line in the graph. df ar= 1x-80 2) Find the general solution to this differential equation. Find the funct...
Find the general solution of the following differential equation. Primes denoto derivatives with respect to x. x(5x + y + y(15x + y) = 0 The general solution is (Type an implicit general solution in the form F(x,y)=C, where is an arbitrary constant. Do not explicitly include arguments of functions in your answer)
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. lf It is exact find a function F(xy whose differential, dF(x y is the left hand side of the differential equation. That is, level curves F x,y) = Care solutions to the differential equation First: M, (x, y) = | 3-e^x(cosy) and N(x, y)3-enx(cosy) If the equation is not exact, enter not exact, otherwise enter in F(x,y) here (-e1xsiny+3y)+(3x-excosy) (1 point) Use the "mixed...
(1 point) Find the general solution of the differential equation x' + 6x = e-41 x= Use C for any arbitrary constant.
1.6.12 Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 5xyy' = 5y2 + 4x 18x2 + y2 For x, y>0, a general solution is (Type an implicit general solution in the form F(x,y) = C, where C is an arbitrary constant. Type an expression using x and y as the variables.)
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, dF(, y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation: dy 4x3 - y dx + 4y2 First rewrite as M(x,y) dic + N(x, y) dy = 0 where M(x,y) = and N(x,y) = If the equation is not exact, enter not exact, otherwise...
(1 point) a. Find a particular solution to the nonhomogeneous differential equation y" + 3y - 10y = ex. yp = help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use cy and c2 in your answer to denote arbitrary constants, and enter them as c1 and c2. Yh = help (formulas) c. Find the most general solution to the original nonhomogeneous differential equation. Use cy and C2 in your answer to denote arbitrary constants....
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
Find the equation of the tangent line to the graph of the function f (x) = sin (777) at the point (-2,0).
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) - C are solutions to the differential equation (-le sin(y)-3y)ax + (-3x + 1e' cos(y))dy-0 First: M,(x,y) = and N,( If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
1. Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function Line f(x) = 2x2 2x − y + 2 = 0 y = 2.Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. f(x) = 2(2 − x)2, (6, 32) f '(6) =