X- = y Consider the following differential equation. dx y Let f(x, y) Find the derivative of f. %3D af ay Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through point (xo, Yo) in the region.

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A: Given differential equation, dydt=51-y100y        ...(1) And y=1001+99e-5t

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Q: dx 3.rye- = -y°. Determine its integrating factor. dy Consider the linear differential equation

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A: We have to find the derivative and a region of the xy-plane for which the given differential…

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Q: 1 dy= and the initial condition y(9) = T. Find function of y Use the differential equation: dx 81 +…

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Q: Q-10. Find the order and degree of the differential dy 4 dx equation dy 7x = 0 (0.5mark) dx

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Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

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A: To find the expression for y(t) and find the limit y(t) as t tends to infinity

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Q: Given the differential equation dy 3x dx Separate the Variables, and then rewrite using Integration…

A: Given the differential equation is dydx = 3xy3

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Q: (a) Find the general solution of the differential equation (dy)/(dx) - (2y)/(x - 2) = (x - 2)3. (b)…

A: (a) Given- dydx-2yx-2=x-23 To find- The general solution of the above differential equations.…

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Q: . Given the differential equation: 3x² cos y dx - sin xdy + 2xdx = y cos x dx + 2x³y sin y'dy, y(0)…

A: Given: The differential equation is 3x2cosy2dx-sinxdy+2xdx=ycosxdx+2x3ysiny2dy. The given step size…

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A: In a differential equation, if the variables can be separated then it is a variable separable…

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A: dydx=fyxu=ux=yxx=yx⇒y=ux⇒dydx=u+xdudxso  dydx=fu=u×xdudx⇒xdudx=fu-u⇒   dufu-u=dxx  Seperable…

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Q: dy Given the differential equation x = y – x sec dx a) Show that the substitution of y=ux transforms…

A: Given the differential equation  x dydx = y - xsecyx   a) By the substitution of y = ux in the given…

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A: A differential equation is basically an equation that relates one or more functions and its…

Q: Given the differential equation dy 1 X · = -+ y dx y i. State whether the differential equation…

A: For (i), A first order separable ODE has the form of Ny·y'=Mxxdydx=1y+ySubstitute dydx with y' ⇒xy'…

Q: dx Find the solution of the differential equation - 2 + x= e with x dr dx dt dx 1 at t=0.

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Q: What is the integrating factor for the differential equation given below? xy dx + (x²y- xy²)dy = 0 a…

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Q: Find a function y = y(x) that has all of the following properties: • It satisfies the differential…

A: We have to find a function y=y(x) that has the following properties. 1) It satisfies the…

Q: ay H) Let y = f(x) be the particular solution to the differential equation dx 3(9 - y) with the…

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Q: -( – 2) (; – y). dy Consider the differential equation dt For what values of y will y(t) be…

A: Given dydt=y-212-y

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Q: 50. The integrating factor of the differential equation x dy + (y - x^2) dx = 0 is.

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Q: Question* The appropriate integrating factor for the following differential equation (2xy? + xy²)dx…

A: here last option is true

Q: The integrating factor of non-exact differential equation (2'y – a°)dr - (y- 2y)dy = 0 %3D 1 rty3 +…

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A: This question can be solved using the concept of linear differential equation. Note: elna=a

Q: =x+x* +1 satisfies the differential equation (x +1): dy Show that y dx

A: Given the given differential equation is x2+1d2ydx2+xdydx-m2y=0 and the given value is y=x+x2+1m.

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Q: Ive the differential equation below over the interval from x = 0 to 1 using a step size 0.2 where…

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