(Question-Solution-Final Answer-Conclusion format) E. Generate solution of the first-order differential equations using different analytic techniques. 3. Exact Differential Equations b. (2xy - tany)dx + (x² − xsec²y)dy = 0

Q: COTE - L J

A: Given query is to find indicated derivative.

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A: See this solution in below.

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A: Length of curve =∫ab1+dydx2dx

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Q: (d) Let y(x) = [tan-¹ (√)]4. Find y'.

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A: The given equation is; (2xy4ey+2xy3+y)dx +( x2y4ey - x2y2-3x)dy=0 y(1)=1.

Q: Se-¹x² dx. е

A: Given query is to find the integral.

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A: Topic- Differential equations We are given that, y''=2x+sin x+ex We know that,…

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A: Given query is to find function is continuous or not on x = 2.

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A: The given differential equation is dydx+ycotx=5ecosx, yπ2=1 This is a linear differential equation…

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A: Determine the Order and Degree of the differential equation.

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A: Determine the Order and Degree of the Differential equation.

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A: Given Data  y(x+y+1)dx + x(x+3y+2)dy =0

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A: Given     Yi^ = 4.8 + 1.3Xi As per the student's request, I am providing the solution to the (c)…

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A: See this solution in below

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A: We can find area of the face .

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A: a) ∆x=b-an

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A: a) Assuming that the size of the fish population satisfies the logistic equationdPdt=rP1-PN

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A: To solve for the value of constant C in  the equation: 2x+3y'=y+2x+312when x=-1, and y=0.

Q: 1 † (OM - ON) - M . If OA es OB. U O D. e-5 ys ly = then what is the integrating factor?

A: Key points: Consider the differential equation M dx + N dy = 0. If this equation is not exact, then…

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A: we need to find out at which of the equations has solution of the form F(x,y)=c

Q: 1) Using the definition, calculate the derivatives of the functions. Then find the values of the…

A: Solve by derivatives

Q: Let f(x)=−3e^x+2+e^4 f′(0)=

A: SOLUTION-