Explanation Theorem used: Separation of Variables: The solution of the differential equation, f ( y ) y ′ = g ( x ) is given implicitly by the equation, ∫ f ( y ) d y = ∫ g ( x ) d x . Calculation: The given differential equation y ′ 1 y = e x is of the form f ( y ) y ′ = g ( x ) where, f ( y ) = 1 y and g ( x ) = e x . By the above theorem, the solution is given by, ∫ f ( y ) d y = ∫ g ( x ) d x ∫ 1 y d y = ∫ e x d x ln | y | = e x + C y = e e x + C Simplify further as, y = e e x <

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Author: Stocker

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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 9.2, Problem 33E

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To find: The general solution for the differential equation y′=yex and its particular solution satisfying the initial condition y(0)=3e.

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Chapter 9.2, Problem 32E

Chapter 9.2, Problem 34E

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Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

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The general solution for the differential equation y ′ = y e x and its particular solution satisfying the initial condition y ( 0 ) = 3 e .

Solution Summary: The author explains the general and particular solution of the differential equation yprime, which is given implicitly by the equation.

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To find: The general solution for the differential equation y′=yex and its particular solution satisfying the initial condition y(0)=3e.

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Chapter 9 Solutions