(2x + 3)y' = y + (2x + 3)/2; when x = –1,y = 0

Q: 1. у" — 4у 3 2+ 3х — х2

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Q: Draw a slope field for the differential equation / = 0.2x² + y

A: We have to draw the slope field for the following differential equation, y'=0.2x2+y

Q: У"(х) — 2у(х) + у (x) — 4x2 — 3 + et

A: Given :         y''(x) - 2y'(x) + y(x) = 4x2 - 3 + exx   To find:            The general solution of…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x-3xy- 2y²…

A: This is a simple question based on differential equations which could be solved using the basic…

Q: Obtain the Differential Equation from the family of lines whose slope is thrice the y- intercept.

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Q: Solve for differential Equation y^2dx+x^2dy=0

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Q: ex 2. y" – 4y' + 3y = - 1+ ex

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Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: Find the 4th order differential of the function y=√2x+1.

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Q: Solve for the differential of y when y= sinzx. x=-, and dx = - 3 2

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Q: Find the differential equation associated with y = clx^2+ c2x + c3

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Q: solve the differential equations by using integrating factor y'= (y/x) + 2x+1.       when ; y(1)= 3

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Q: y' + 3y = 8

A: Given differential equation is  y'+3y = 8

Q: Find the general solution of the differential equation. y (4) - y = 8t + cost.

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Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Solve the differential cquation d'y by using the method of variation of parameters.

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Q: Solve the differential equation 2xyy' = 1 + y". If y = 3 when x = 2, determine y when x = 1.

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Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: Find the particular solution to the differential equation. 2y2 dx = 9x2 dy when x = 2, y = -3

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Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

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Q: Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: The differential equation of the family of straight line with the algebraic sum of the intercept…

Q: Q5: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Given the differential equation is y''-5y'+6y = x2e-2x

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: 3x + y + z = 0; z(0) = −1

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Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: Find y2 for differential equation if yI is given: ху" — 20у'%3D 0 Y1 = 15x13 -

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Q: 4.y = C₁e-2x + C₂e³x

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Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

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 for the differential eq   (8x−10xy+4y^2sin^2 (x) )dx=(2ysin2x+5x^2−4xy)dy

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: (9x^2 + y - 1) - (4y - x)y′ = 0

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Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: Find the differential of the given functions. 1. y= x-2x² + 5 5. у 3 1- -s2

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Q: Find the differential of y² + x = 4.

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

Q: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

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Q: What is the solution of the partial differential equation X

A: x∂z∂x+y∂z∂x=z is first order partial differential equation. For solution we use Lagrange's method…

Q: ydx+(2x1/2y1/2-x)dy=0  solution of differential equation

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Q: Find the equation of the line tangent to y = x2 – 3x – 5 and parallel to the line y = 3x – 2.…

A: Explanation of the answer is as follows

Q: solve for Differential Equation y(x2+2)dx - (x2-x)dy = 0 when x= sqrt 3 and  y= 1/3

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Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: Use separation of variables to find the general solution of the differential equation. ely' = 3x5 +…

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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: What is the differential equation of family of parabolas with vertex on the x – axis and axis…

A: General equation of parabola parallel to y-axis and having center (h, k) and having distance 'a'…

Q: 5. Find the solution of the differential equation using Variation of Parameters. y"' – 3y" + 3y' =

A: We will use the method of variation of parameters to solve this question. First, we find the three…

Q: Find a special solution of yn+2 - Yn= fo = constant by variation of parameters.

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Q: Solve the differential equation by the method of variation of parameters. y"+3y'+2y=1/(1+ex)

A: The differential equation is given by,