Show that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation. x²y³ + x(3+ y²y = 0. (x, y) = Here, M(x, y) = x³y and N(x, y) N- Therefore, M, - Therefore, M, and N, - N.. Integrating M with respect to x, we see that - .We see that the equation is not exact. Now, multiplying the equation by u(x, y), the equation becomes x dx +( h(y) -N- +h(y). Further, Therefore, h(y)- dy 0. Now we see that for this equation M-x and and we conclude that the solution of the equation is given implicitly by and y 0.
Show that the given equation is not exact but becomes exact when multiplied by the given integrating factor. Then solve the equation. x²y³ + x(3+ y²y = 0. (x, y) = Here, M(x, y) = x³y and N(x, y) N- Therefore, M, - Therefore, M, and N, - N.. Integrating M with respect to x, we see that - .We see that the equation is not exact. Now, multiplying the equation by u(x, y), the equation becomes x dx +( h(y) -N- +h(y). Further, Therefore, h(y)- dy 0. Now we see that for this equation M-x and and we conclude that the solution of the equation is given implicitly by and y 0.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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