(a) Use the family of solutions in part (a) of to find an

Chapter 1, Problem 34E

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QUESTION:

(a) Use the family of solutions in part (a) of Problem 33 to find an implicit solution of the initial-value problem y dy/dx = 3x, y(2) = -4. Then, by hand, sketch the graph of the explicit solution of this problem and give its interval I of definition

(b) Are there any explicit solutions of y dy/dx = 3x that pass through the origin?

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QUESTION:

(a) Use the family of solutions in part (a) of Problem 33 to find an implicit solution of the initial-value problem y dy/dx = 3x, y(2) = -4. Then, by hand, sketch the graph of the explicit solution of this problem and give its interval I of definition

(b) Are there any explicit solutions of y dy/dx = 3x that pass through the origin?

ANSWER:

Step 1 of 4

The given differential equation will be

        

Rewrite the above equation, we get

        

Integrate both the sides

        

So,

        

 

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