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(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given the first order IVP y 0, х21 (1) Find the explicit solution on the interval 0 < x < 1 У(х) %3 (2) Find the lim y(x) = х—1 (3) Then find the explicit solution on the interval x 1 У(х) —
1. 10 points Given y(x) x 'is a solution to the differential equation x’y"+ 6xy'+6y=0 (x > 0), find a second linearly independent solution using reduction of order.
Find a solution 9. y(3) – 6y"+11y'- 6y=0, y(0)=y'(0)=0, y"(0) = 3.
Solve the given differential equation with initial condition. y'-6y = 0, y(0) = 9 The solution is y(t) = (Type an exact answer.)
(1 point) Find the solution of Y" – 6y' +9y = 144 91 with y(0) = 2 and ý (0) = 3. y =
1. (4 points) Determine whether the given function y, given explicit or implicit, is a solution to the corresponding differential equation a) y = 2* +3e2a; y" - 3y + 2y = 0. dy 2.ry b) y - In y = r2+1, (Use implicit differentiation) dr y-1 2. (3 points) Find the solution to the initial value problem: dy = e(t+1); y(2) = 0 dr 3. (3 points) Find the general solution to the following equation. y dy ada COS
Consider the following. x' = 6x − 10y y' = 10x − 6y, X(0) = (6, 10) (a) Find the general solution. (x(t), y(t)) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) (b) Find the solution satisfying the given initial condition. (x(t), y(t)) = (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
In problems 7 and 8 find the solution of the given initial value problem in explicit form: 7. sin 2.x dx + cos 3y dy = 0, y /2) = 1/3. 8. y' (1-22)/2 dy = arcsin x dx, y(0) = 1.
1. (each 5pts) Find the solution of the following differential equations. (a) y" + 6y' +9y=0 which satisfies yo)= 4 and V = 4 (b) v- 5y' +6y=0 which satisfies y(o)=1 and y (0)=2
Find the solution of the given initial value problem. (4) – 6y'"' + 9" = 0 y(1) = 10 + e, y' (1) = 8 + 3e3, y" (1) = 9e), y'' (1) = 27e3 y (1)