The differential equation can be written in differential form: where M(x, y) -y-2y^7 y + 2y¹ = (y² + 6x) y' M(x, y) dx + N(x, y) dy = 0 , and N(x,? y) = y^4 + 6x The term M(x, y) dx + N(x, y) dy becomes an exact differential if the left hand side above is divided by y7. Integrating that new equation, the solution of the differential equation is = C.

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

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A: The solution is given as

Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

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A: Solution :

Q: 3. Describe the qualitative behavior of the differential equation x= x³-x by locating all the…

A: Equillibrium Points