Question

1. Use Euler’s method with step size ∆x = 1 to approximate y(4), where y(x) is the solution of the initial value problem:

y' = x^{2}+ xy

y(0) = 1

2. The coroner arrives at a murder scene at 9:00 pm. He
immediately determines that the temperature of the body is 83◦F. He
waits one hour and takes the temperature of the body again; it is
81◦F. The room temperature is 68◦F. **When was the murder
committed?** Assume the man died with a body temperature
98◦F. (Hint: Newton’s Law of Cooling)

Answer #1

The coroner arrives at a murder scene at 9:00 pm. He immediately
determines that the temperature of the body is 83◦F. He waits one
hour and takes the temperature of the body again; it is 81◦F. The
room temperature is 68◦F. When was the murder
committed? Assume the man died with a body temperature
98◦F. (Hint: Newton’s Law of Cooling)

Use Euler’s method with h = π/4 to solve y’ = y cos(x) ,
y(0) = 1 on the interval [0, π] to find y(π)

Use Euler's method with step size 0.1 to estimate y(0.5), where
y(x) is the solution of the initial-value problem
y'=3x+y^2, y(0)=−1
y(0.5)=

dy/dx = x^4/y^2
initial condition y(1)= 1
a) use eulers method to approximate the solution at x=1.6 and
a step size od delta x = 0.2
b) solve the differential equation exactly using seperation
variabled and the intial condtion y(1)=1.
c) what is the exact value of y(1.6) for your solution from
part b.

g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3,
x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and
yt(3,4)=-100.
Calculate gs(3,4)

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

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