Question

find the solution for the DE

dy/dt +ty^3 +y/t = 0

answer explicitly if passible

Answer #1

**Please comment if you have any doubt.**

Find the general solution to the given differential
equation. 1+(1+ty)e^ty+(1+t^2e^ty) dy/dt=0

solve the given initial value problem. y(cos2t)e^ty -
2(sin2t)e^ty + 2t + (t(cos2t)e^ty - 3) dy/dt = 0, y(0)=0

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

Are both of the following IVPs guaranteed a unique solution?
Explain. (a) dy/dt =y^ 1/3sin(t), y(π/2)=0. (b) dy/dt =y^1/3
sin(t), y(π/2)=4.

Find the general solution of the system
dx/dt = 2x + 3y
dy/dt = 5y
Determine the initial conditions x(0) and y(0) such that the
solutions x(t) and y(t) generates a straight line solution. That is
y(t) = Ax(t) for some constant A.

dx/dt - 3(dy/dt) = -x+2
dx/dt + dy/dt = y+t
Solve the system by obtaining a high order linear differential
equation for the unknown function of x (t).

Find the general solution of the equation.
d^2y/dt^2-2t/(1+t^2)*dy/dt+{2/(1+t^2)}*y=1+t^2

a). Find dy/dx for the following integral.
y=Integral from 0 to cosine(x) dt/√1+ t^2 ,
0<x<pi
b). Find dy/dx for tthe following integral
y=Integral from 0 to sine^-1 (x) cosine t dt

Find a general solution to the given equation for t<0
y"(t)-1/ty'(t)+5/t^2y(t)=0

Co nsider the IVP dy/dt= 1+ ty, 1≤ t ≤ 2, y(1)=2 with
h=0.3. Using Heun's method;
Then y(1.3)=
A)1.528
B)2.107
C)3.152
D)1.753

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