Question

find the solution to the following ivp

dy/dy-2ty=6t^2e^(t^2),y(0)=5

Answer #1

Solve the differential equation (3y^2+2ty)+(2ty+t^2)dy/dt=0

Solve the following differential equations
1. cos(t)y' - sin(t)y = t^2
2. y' - 2ty = t
Solve the ODE
3. ty' - y = t^3 e^(3t), for t > 0
Compare the number of solutions of the following three initial
value problems for the previous ODE
4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0
Solve the IVP, and find the interval of validity of the
solution
5. y' + (cot x)y = 5e^(cos x),...

MATLAB
Create an M-File for this IVP,
dy/dt =
t^2 - 16*sin(t), y(0) = 0 and create an anonymous function
g so that it evaluates the slope field at points of our new
ODE.
Ensure you use commands of using a for loop to plot the exact
solution for the IVP in this exercise as well as the Euler
approximations for Δt=0.5, Δt=0.25, and Δt=0.125 all on the same
graph.

Find derivative for the following :
1- m(t) =-3t (6t^4 -1)^5
m'(t) =
2- y= (3x+2)^5 (4x+1)^-3
dy/dx
3- y= (10x^2 - 20x +20) e^-4x

Initial value problem
dy/dt=(6t^5/1+t^6)y+7(1+t^6)^2 y(1)=8

5.
Find a general solution of t^2x′′ − 5tx′ + 5x = 6t^3, t > 0
using the method of undetermined coefficients

Show that the IVP
dy/dx = xy^(3/2)
y(2) = 0
has a solution but it may or may not be unique (i.e. the
Existence and Uniqueness Theorem doesn’t
imply uniqueness). (Remark: Make sure to draw an appropriate
rectangular region.)

Find the general solution to the following:
[(e^t)y-t(e^t)]dt+[1+(e^t)]dy=0

solve ivp: (y+6x^2)dx + (xlnx-2xy)dy = 0, y(1)=2, x>0

The function y1(t) = t is a solution to the
equation.
t2 y'' + 2ty' - 2y = 0, t > 0
Find another particular solution y2 so that
y1 and y2 form a fundamental set of
solutions. This means that, after finding a solution y2,
you also need to verify that {y1, y2} is
really a fundamental set of solutions.

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