   Chapter 4.5, Problem 32E

Chapter
Section
Textbook Problem

Differential Equation In Exercises 31-34, find the general solution of the differential equation. d y d x = 10 x 2 1 + x 3

To determine

To calculate: General solution of given differential equation dydx=10x21+x3.

Explanation

Given:

dydx=10x21+x3

Formula used:

If f'(x) is derivative of f(x) then

f'(x)dx=f(x)

According to theorem for change of variable for indefinite integrals

If u=g(x) then du=g'(x)

Then integral will take the following form

f(g(x))g'(x)dx=f(u)du=F(u)+C

Calculation:

To find the general solution of given equation we have to integrate the equation with respect to x

On integrating equation with respect to x we get

dydxdx=10x21+x3dxy=10x2

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