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Chapter 1: Q3 E (page 13)

In Problems 3-8, determine whether the given function is a solution to the given differential equation.

y=sinx+x2,d2ydx2+y=x2+2

Short Answer

Expert verified

The given function is a solution to the given differential equation.

Step by step solution

01

Differentiating the given equation w.r.t. (with respect to) x

Firstly, we will differentiatey=sinx+x2 with respect to x,

dydx=cosx+2x

Again, differentiating with respect to x,

d2ydx2=-sinx+2

02

Simplification

Putting the values from step 1 in the L.H.S. (Left-hand side) of the given differential equation,

d2ydx2+y=-sinx+2+sinx+x2d2ydx2+y=x2+2

Which is the same as the R.HS. (Right-hand side) of the given differential equation.

Hence,y=sinx+x2 is a solution to the differential equationd2ydx2+y=x2+2.

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Newton鈥檚 law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, dTdt=KMt-Ttwhere K is a constant. Let K=0.04min-1and the temperature of the medium be constant, Mt=293kelvins. If the body is initially at 360 kelvins, use Euler鈥檚 method with h = 3.0 min to approximate the temperature of the body after

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