
Please help out! I will rate thank you b) Solve the following ODE using the substitution,...
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
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1. a) Solve the following linear ODE. dy + 2y = 4x? dx X X>0
PLEASE. ANSWER ONLY IN MATHEMATICA, THESE PROBLEMS CAN ONLY BE
DONE IN MATHEMATICA. I NEED THEM TO BE DONE STRICTLY IN
MATHEMATICA. WILL DOWN VOTEIF NOT DONE IN MATHEMATICA!!!!! (thank
you in advance)
Lab Exercise 1. Solve: (4xy3 - cos y -e ")dx + (6x2y* +xsin y 3) dy 0 2. Solve the initial value DE: (Cos(x)Sincx)- xy2 )dk + y(l-)dy-0, y(o)-2 3. a. Determine a function M(x y) so that the following DE is exact: Mx, y) dx +(xe+...
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.
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21
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b) dy 1 X>0 dxx-x,
2. Solve the following ODEs using an appropriate method. a) (ex + 1) .y = ev sin x b) dy 1 = -y - dx y=x. x > 0 c) (2x2y3 + 3y2) dy = -xy4 dx Cid
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Solve the Cauchy problem for the diffusion equation ut = Uxx, xe (-0, 0), t > 0 (b) u(x,0) = x for x € (-1,1) and u(x,0) = 0 for other values of x.
# Q(1) SOLVE A SIMPLE ODE # the ODE, dy/dx + y = x, y(0) = 1 can be analytically solved to get # the equation y(x) = x + 2*exp(-x) - 1. # Show that you can use ODEINT to match that performance using pyplot This is in python
please solve and show work clearly for both a and b
Use an appropriate substitution to solve the given differential equation. 4. a) (x3y) dx - (3x +y) dy = 0 b) y(x +y+ 1)2 dr