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Fundamentals Of Differential Equations And Boundary Value Problems
Found in: Page 79
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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Short Answer

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

x2-2y-3dy+2xy-3x2dx=0

The solution of the given equation is x2y-x3+y-2=C.

See the step by step solution

Step by Step Solution

Step 1: Given information and simplification

Given that, x2-2y-3dy+2xy-3x2dx=01

Let us check whether the given equation is exact or not.

Then, M=2xy-3x2,N=x2-2y-3.

Differentiate the value of M and N.

My=2xNx=2xMy=Nx

So, the given equation is exact.

Step 2: Evaluation method

Now, let us assume M=Fx=2xy-3x2.

Integrate on both sides.

F=2xy-3x2dx=x2y-x3+gy

Differentiate the F with respect to y.

Fy=x2+g'y=N

Equalise the values of N.

x2+g'y=x2-2y-3g'y=-2y-3

Integrate on both sides.

g'y=-2y-3dygy=y-2+C1

Substitute in equation of F.

x2y-x3+y-2+C1=0x2y-x3+y-2=C

So, the solution is role="math" localid="1664022924236" x2y-x3+y-2=C

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