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Chapter 2: Q1E (page 64)

In problems Classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.

(x2y+x4cosx)dx-x3dy=0

Short Answer

Expert verified

The equation is linear.

Step by step solution

01

Find if the equation is separable 

Here

(x2y+x4cosx)dx-x3dy=0dydx=(x2y+x4cosx)x3

This equation cannot be written in the form as g(x) h(y).

so, this equation is not separable.

02

Determine if the equation is linear

The equation can be written as

dydx-yx=xcosx

Now,P(x)=-1x,Q(x)=xcosx

This equation is a linear.

03

Evaluate whether the equation is exact

The condition for exact is 鈭�M鈭�y=鈭�N鈭�x.

M(x,y)=x2y+x4cosxN(x,y)=-x3

鈭�M鈭�y=x2鈭�N鈭�x=-3x2鈭�M鈭�y鈮�鈭�N鈭�x

Hence, the equation is linear.

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Most popular questions from this chapter

Use the method discussed under 鈥淗omogeneous Equations鈥� to solve problems 9-16. dxdt=x2+tt2+x2tx

Question: In Problems 31-40, solve the initial value problem.

2y2+4x2dx-xydy=0,鈥夆赌�y1=-2

Use the method discussed under 鈥淓quations of the Form dydx=Gax+by鈥� to solve problems 17-20.

dydx=x+y+22

Question: In Problems 31-40, solve the initial value problem.

t+x+3dt+dx=0,鈥夆赌夆�夆赌�x0=1

Question: In Problems 1-30, solve the equation.

鈥�yx-y-2dx+xy-x+4dy=0
See all solutions

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