If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

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Q: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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Q: Suppose that f(t) is a solution of the differential equationy′ = ty - 5 and the graph of f(t) passes…

A: Given, y'=ty-5 And f(t) is a solution of the differential equation. The graph of f(t) passes through…

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: 7. Find the particular solution of the differential equation dx +5x³y x³ passing through the point

A: Given, dydx+5x3y=x3,   0,72 it is a linear differential equation p(x)=5x3,  q(x)=x3…

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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Q: 4. Solve (D-1)y (x'+2x +x+6)e using differential operators method.

A: Consider a homogenous differential equation: ay''+by'+cy=0 Write an auxiliary equation corresponding…

Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

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Q: Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

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Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the particular solution first.

Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

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Q: Example 35. Using th d²y satisfying the differential equation v(1) = 2. + y = x, subject to the…

A: Here we need to use finite difference mthod.

Q: at

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Q: What is the particular solution to the differential equation y -2x 3y2 – 2 with y 1 when dy x= 1?

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Q: Find the particular solution of the differential equation    y′ + sin x cos x = 0    that satisfies…

A: Consider the given differential equation: y'+sinxcosx=0 ; yπ=-2 Here, the objective is to find the…

Q: If 2x3+3ycos(xy)+(cx2y2+3xcos(xy))y'=0 is the exact differential equation then c =?

A: The exact differential equation is defined as the differential equation of the form Mx,ydx+Nx,ydy=0,…

Q: Find x for which the line tangent to the parabola y = 4x – x2 is horizontal.

A: In this question, we need to find the value of x at which the tangent line is horizontal.

Q: Example 9: Obtain the differential equation of the co-axial circles of the svstem x² +y² + 2ax+c² =…

A: Answer:

Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

Q: A population of wild horses is represented by the logistic differential equation dP/dt =…

A: Given: The logistic differential equation is, dpdt=0.08p-0.00004p2          (1) To find: A) The…

Q: Find the point on the curve y = x3 – 3x for which the tangent line is parallel to the x-axis.

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Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: The rate of growth of a plant is proportional to the difference between its height h and the maximum…

A: The given data is: The rate of growth of a plant is proportional to the difference between its…

Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that  The differential equation  To find the particular solution of the differential equation

Q: Solve the Euler-Cauchy differential equation dy -3x + 4y = dx In?x - Inx

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Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

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Q: 4. Solve (D -1)y =(x +2x* +x+6)e" using differential operators method.

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Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

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Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: Determine the general solution of the differential equation y′′ - 4ky′ + 4k2y = ex, with k real…

A: In this question, concept of solution of differential equation is used. General equation of…

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

A: The given data is: N=74x-x2 To use differential approximation to estimate the increase in sales that…

Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: Without solving explicitly, classify the critical points of the autonomous differential equation dx…

A: See the solution and follow the steps. You will understand easily.

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

A: Given solution is xy=aex+be-x+x2 find DE by eliminating arbitrary constants

Q: Let y' – 35y = 7x*e5x. Is this differential equation pure-time, autonomous, or nonautonomous?

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Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: 19, 4. 6. Given that the differential equation xy" + xy'- y = 0 has a solution yı=x. Use the

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

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Q: 4. Solve (D-1)y=(x'+2x+x+6)e using differential operators method.

A: Given: D2-1y=x3+2x2+x+6e2x

Q: 3. Solve the Euler-Cauchy differential equation d²y dy 3x +4y= ln² x – In x dx² dx

A: Given an Euler-Cauchy differential equation, x2y"-3xy'+4y=ln2x-lnx Re-writing it in the standard…

Q: Q3: if y'-f(y/x) where v-y/x Find a solution to the differential equation 2xyy'-y2+x2 =0 ?

A: Given

Q: Suppose the motion of a mass-spring system is described by the differential equation x"+By'+1y=0.…

A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…