Given the function y = x3 + x² + x + 10, suppose x increases from 1 to 1.1. Find the absolute error and percentage error that result if we approximate the resulting change in y using the differential formula.

Q: use the variation-of-parameters method to solve the given differential equation. Q. y′′+y =tanx.

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Q: Find the value of k so that the given differential equation will be exact

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Q: Find the general solution of the following differential equation (and check your answers by…

A: Given differential equation is y''=-2xy'2 let y'=t y"=dt So ,dt=-2xt2dx Integrating both sides,we…

Q: Straight lines with slope half the value of the x-intercept

A: The equation of a line is defined as y=mx+b, where, m is the slope and b is the y-intercept.

Q: Find general solution for the following linear differential equation: y' + 2ty = 4t.

A: Given that: y'+2ty=4t

Q: Find the general solution of the differential equation. y′ = arctan x/ 2

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Q: ordinate at x = 3. 36. Solve the differential equation (x-2)(x+3)-- (2x+1)3D0 given that y= In6 when…

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Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: For what values of r does the function y= e™* satisfy the differential equation y"- 4y'+ 2y = 0?

A: for the homogeneous differential equation, the auxiliary equation is  compare this equation with…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: e. Cxy +C'x + 9 = 0

A: Cxy+C2x+9=0

Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: Find the value of n such that when the differential equation (x+y^3)dx+6xy^2dy =0 is multiplied by…

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Q: Find the differential equation of the exponential curve y = A(33x) where A is an arbitrary constant.…

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Q: When à = 0 the differential equation becomes X" = 0 which gives the solution X = ax + b.

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Q: Obtain the differential equation associated with the primitive y = Ae3x + Be2x + Ce*.

A: Given differential equation is we have to obtain the differential equation associated with the…

Q: y se, SinX+G Cnn

A: Explanation of the answer is as follows

Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

Q: For non-negative PP, look at the differential equation:  dP/dt=-0.1P(1-P/200)  What are the…

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Q: Suppose you have the differential equation: y' + p(x)y ln(y) = q(x)y. Prove that the substitution v…

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Q: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: The following differential equation satisfies the following initial condition y(0)=-3. ydy-xdx-0…

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Q: Find the differential equation whose general solution is y = cvh x + cv2 e^x %3D

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Q: Consider the following quantity, D = 2(x² + y?) By finding its differential equation, show that the…

A: It is given that

Q: SOLVE FOR THE PARTICULAR SOLUTION of the differential equation: dy a yax (1+) where a and b are…

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Q: 4.y = C₁e-2x + C₂e³x

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Q: In the following problems, obtain the differential equations of the given families of curves whose…

A: All circles passing through the origin and 0, 4. Let the equation of the circle be x-h2+y-k2=r2. Now…

Q: Find a differential equation whose general solution is y = cie" + cze *. = 0

A: To find a differential equation whose general solution is given by, y=c1e7t+c2e−3t

Q: (1) When sugar is dissolved in water, the amount A that remains undissolved after t minutes…

A: We have to find the time taken for half of sugar to dissolve.

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: y = Ax² + Be*

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Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

Q: Suppose that the number x(t) (with t in months) of alliga- tors in a swamp satisfies the…

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Q: Solve the Linear Higher Order of differential equation using the formulas below. (D² – D + 3)(x In…

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Q: Find the differential equation which has y= asinx+bcosx+xcosx

A: Given: y=asinx+bcosx+xcosx                                   ..1 for finding differential equation…

Q: Is the given Differential Equation a homogenous? If yes, what is the degree?

A: We know that a differential equation containing a homogenous function is called a homogenous…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: Assume that the rate of change of y is proportional to y. Solve the resulting differential equation…

A: We have to find the equation that passes through the given points.

Q: Suppose that the population P(t) of a country satisfies the differential equation dP/dt= kP(200 - P)…

A: dPP(200-P)=kdt∫dPP(200-P)=k∫dt1200∫dPP-∫dP200-P=k∫dtInP-In(200-P)=200kt+cInP200-P=200kt+cP200-P=ce20…

Q: Find the value of the constant(s) so that the function x (t) = emt is a solution of the Differential…

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Q: y = cje + c2er

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Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: 4. x" +x=e+!.

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Q: What is the general solution to the differential equation ydx - ( x - sqrt(x² + y² )dy = 0?

A: Let's find.

Q: Find the salution of the following differential equationss © ý=ytanh(x)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find the general solution of the following differential equation if one solution is known to be y=x…

A: Using the reduction of order

Q: Find the value of n such when the differential equation (x + y3)dx + 6xy2dy = 0 is multiplied by xn…

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Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)x2y is an…

A: Here given differential equation as dydx=12x2yordyy=x2dx2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.