#3 (d) Find an explicit solution y(«), by using the given substitution then solving a linear...
1. a) Solve the following linear ODE. dy * dx + 2y = 4x2, x > 0 b) Solve the following ODE using the substitution, u = dy (x - y) dx = y c) Solve the Bernoulli's ODE dy 1 + -y = dx = xy2 ; x > 0
Find an explicit solution of the given initial-value problem. ✓ 3 ✓ 1 - y2 dx - V1 - x? dy = 0, y(O) = 2
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
just focus on A,B,D 1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
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 point) An equation in the form y + p(x)y -(x)y with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution wich transforms the Bernoulli equation into the following first order linear equation for v: Given the Bernoulli equation we have n- We obtain the equation u' Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by Then transforming back into the variables...
Please help out! I will rate thank you b) Solve the following ODE using the substitution, u = dy (x - y) = y A c) Solve the Bernoulli's ODE dy 1 dx + y = xy2 ; x > 0
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
A) Find the solution of the given 2nd order Homogenous ODE using undetermined coefficient 1) y"-10y, + 25y-30x + 3 4 3) y"- 16y - 2e4x 4) y" + 2y'ysin x + 3 cos 2x B) Find the solution of the given 2nd order Homogenous ODE using variation parameter 1) y" + y sec θ tan θ 1+e 3) 3y''-6y' + 6y = ex secx x+1 A) Find the solution of the given 2nd order Homogenous ODE using undetermined coefficient...
Find an explicit solution of the given initial-value problem. V1 - y2 dx - V1 – x2 dy = 0, 7(0) = 1) =