Explanation Calculation: The differential equation is given by, y ′ = F ( a x + b x + c ) ... ( 1 ) The equation of V is given as, V = a x + b y + c ... ( 2 ) Substitute V for a x + b y + c in equation ( 1 ) . y ′ = F ( V ) d y d x = F ( V ) ... ( 3 ) Differentiate the equation ( 2 ) with respect to x . d d x ( V ) = d d x ( a x + b y + c ) d V d x = a + b d y d x + 0 b d y d x = d V d x − a d y d x = 1 b ( d V d x − a ) Substitute 1 b ( d V d x − a ) for d y d x in equation ( 3 )

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 1.8, Problem 53P

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Whether the change of variables from x, y to x, V, reduces equation y′=F(ax+bx+c) to the separable form is 1bF(V)+adV=dx.

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Chapter 1.8, Problem 52P

Chapter 1.8, Problem 54P

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Differential Equations and Linear Algebra (4th Edition)

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To check: Whether the change of variables from x , y to x , V , reduces equation y ′ = F ( a x + b x + c ) to the separable form is 1 b F ( V ) + a d V = d x .

Solution Summary: The author compares the equation of (2) and V.

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To check:

Whether the change of variables from x, y to x, V, reduces equation y′=F(ax+bx+c) to the separable form is 1bF(V)+adV=dx.

Want to see the full answer?

Chapter 1 Solutions

To check: Whether the change of variables from x , y to x , V , reduces equation y ′ = F ( a x + b x + c ) to the separable form is 1 b F ( V ) + a d V = d x .

Solution Summary: The author compares the equation of (2) and V.

Concept explainers

Videos

To check: Whether the change of variables from x, y to x, V, reduces equation y′=F(ax+bx+c) to the separable form is 1bF(V)+adV=dx.

Want to see the full answer?

Chapter 1 Solutions

To check:

Whether the change of variables from x, y to x, V, reduces equation y′=F(ax+bx+c) to the separable form is 1bF(V)+adV=dx.