Each of the differential equations in Problems 31 through 36 is of two different types considered in this chapter–separable, linear, homogeneous, Bernoulli, exact, etc. Hence, derive gen- eral solutions for each of these equations in two different ways; then reconcile your results. dy 31. dx 3(y + 7)x²

Q: In each of Problems 6 through 11, determine what type of differential equation of order one…

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Q: For each differential equation in Problems 1-21, find the general solution by finding the…

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Q: A. In each of Problems 1 through 10, solve the given equations using linear differential equations.…

A: The differential equation given to us is y'=cscx+ycotxy'-ycotx=cscx

Q: 41. y' + (1/t)y= 3 cos 2t, t> 0

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Q: A. In each of Problems 1 through 10, solve the given equations using exact differential equations.…

A: Given: 2xydx+y2+x2dy=0

Q: I.In each of Problems 23 through 30, use the method of reduction of order to find a second solution…

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Q: In each of Problems 10 through 11, determine the values of r for wh differential equation has…

A: Here we have,  10) y''+y'-6y=011) y'''-3y''+2y'=0

Q: 7. y' = (4 - ty)/(1+ y²)

A: We are given a differential equation  y'=4-ty1+Y2.............(1) We need to draw the slope field…

Q: Each of the differential equations in Problems 31 through 36 is of two different types considered in…

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Q: A. In each of Problems 1 through 10, solve the given equations using exact differential equations.…

A: Given: 1-xy-2dx+y2+x21-xy-2dy=0

Q: In each of Problems 1 through 12: (a) Draw a direction field for the given differential equation.…

A: The differential equation is y'-2y=t2e2t. (a) Sketch the direction field of the equation as follows.

Q: Solve the following differential equations (DEs) or initial values problems (IVPS): (b) 2xy x²+1 –…

A: The way of finding the value of constant 'C' is

Q: Each of the differential equations in Problems 31 through 36 is of two different types considered in…

A: We have given diferential equation dydx=xy3-xy and we have to find general solution of this equation…

Q: In this problem, y = c,ex + c,e=x is a two-parameter family of solutions of the second-order D…

A: Given y"-y=0 and the initial conditions are y(1)=0 and y'(1)=e To find the general solution for the…

Q: C. In each of Problems 6 through 15, determine what type of differential equation of order one the…

A: Given,x(x2+1)y'+2y=(x2+1)3, when x=1, y=1The given equation is a ordinary linear differential…

Q: A. In each of Problems 1 through 10, solve the given equations using exact differential equations.…

A: given,          y2-2xy+6xdx-x2-2xy+2dy=0   when x=1, y=2

Q: In each of Problems 1 through 6, determine the order of the given differential equation; also state…

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Q: A. In each of Problems 1 through 10, solve the given equations using linear differential equations.…

A: y-x+xy cotxdx+x dy=0 On simplification, we get ⇒x dy=-y-x+xy cotxdx⇒x dy=x-y-xy cotxdx⇒dydx=x-y-xy…

Q: C. In each of Problems 6 through 15, determine what type of differential equation of order one the…

A: The type of the differential equation can be determined with the help of the simplification of the…

Q: In each of Problems 1 through 12: abe (a) Draw a direction field for the given differential…

A: Step:-1 Part (a):- Given that  1+t2 y' + 4t y =1+t2-2 1+t2 y' + 4t y =1+t2-2⇒1+t2 y' =11+t22 -4t y…

Q: 7. yy' = (x + xy²)e²²

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Q: d'y 3-d + dt + dy + +y=1 de

A: Given differential equation is ,    d4ydt4+d3ydt3+d2ydt2+dydt+y = 1 (.)  Order of a differential…

Q: A. In each of Problems 1 through 10, solve the given equations using linear differential equations.…

A: A first order linear ODE has the form y'(x)+p(x)y=q(x)we can rewrite the equationy'+2xy=x3Integraton…

Q: A. In each of Problems 1 through 8, solve the given equations using separable differential…

A: Given: dxdt=1xet+2x

Q: B. In each of Problems 9 through 15, solve the given equations using homogeneous differential…

A: The differential equation is given as (xy+y2)dx-x2dy=0 It can be rewritten as x2dy = (xy+y2)dxdydx =…

Q: B. In each of Problems 9 through 15, solve the given equations using homogeneous differential…

A: Given The given equation is dxdt=x2+tt2+x2tx.

Q: A. In each of Problems 1 through 10, solve the given equations using exact differential equations.…

A: Given: xy2+y-xdx+xxy+1dy=0  when x=1, y=1

Q: 11. d = 4√xy dy dz

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Q: In each of Problems 1 through 10, solve the given equations using linear differential equations. 1.…

A: y'=x-2y solver differential equation       Since multiple questions are asked , Answering first…

Q: In each of Problems 13 through 20, verify that each given function is a solution of the differential…

A: The given differential equation is y''-y=0 The objective is to verify that y1(t)=et, y2(t)=cos ht…

Q: For each differential equation in Problems 1–21, find the general solution by finding the…

A: First I have written the differential equation into operator form and then solved it.Final solution…

Q: B. In each of Problems 9 through 15, solve the given equations using homogeneous differential…

A: In the given question we have to solve the given differential equation s.t…

Q: In each of Problems 1 through 4, determine the order of the given differential equation; also state…

A: 1+y2d2ydt2+t·dydt+y=et

Q: In each of Problems 7 through 10, draw a direction field for the given differential equation. Based…

A: given differential equation  y'=y4-y                   ...i claim- draw a direction field for the…

Q: In each of Problems 1 through 12: (a) Draw a direction field for the given differential equation.…

A: The differential equation y' + 3y=t + e-2t. That is y'=-3y+t+e-2t.

Q: Each of the differential equations in Problems 31 through 36 is of two different types considered in…

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Q: Find general solutions (implicit if necessary, explicit if conve- nient) of the differential…

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Q: A. In each of Problems 1 through 10, solve the given equations using linear differential equations.…

A: we have ;  (y+1)dx+(4x-y)dy=0 ; when x=4'y=4

Q: In each of Problems 19 through 21, verify that the functions y1 and y2 are solutions of the given…

A: The given system is, y''+4y=0,y1(t)=cos2t,y2(t)=sin2t. Write the homogeneous solution.…

Q: (2.ry² – 2y)d.x + (3.x²y – 4x)dy = 0

A: solution :-

Q: 4: Classify and find the general solution of four of the following differential equations: de =x+ dy

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Q: In Problems 39, 40, 41, 42, 43, and 44, y = c1 cos 2x + c2 sin 2x is a two-parameter family of…

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Q: Problem 9 Find the general solution of the differential equation- dy = 2t(y? + 9) Problem 10 dy Find…

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Q: In Problems 31 through 42, verify that the given differential equation is exact; then solve it. 38.…

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Q: B. In each of Problems 9 through 15, solve the given equations using homogeneous differential…

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Q: A. In each of Problems 1 through 8, solve the given equations using separable differential…

A: Given: dxdt=3xt2

Q: Problems 23 and 24 are like Problems 21 and 22, but now use a computer algebra system to plot and…

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Q: each of Problems 23 through 25, find the Wronskian of two solutions of the given differential…

A: Using Abel's formula

Q: Problem 3. Does the following differential equation: dy da 1- y always have a unique solution for…

A: We will use existence and uniqueness theorem here . Existence of solution If f is continuous on an…

Q: B. In each of Problems 9 through 15, solve the given equations using homogeneous differential…

A: Given differential equation is, 2txdx+t2-x2dt=0 This equation can be rewritten as, dxdt=x2-t22tx…