Let (x, Y,) be the solution of the following equations (2x)" = (3y)m3 3Inx = 2lny In 2 %3| %3D Then is

Q: The solution of the 2" order IVP y" - y = 0, y(0) = 0 and y' (0) = 1 is

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Q: 24- ex +12x²-6,yc0)=2, yo)=3

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Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: . Find out optimum solution of the following LPP. Max Z= 2X + 5Y Subject to: 6X + 5Y

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Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: Find two linearly independent solutions to x2y′′+x(3−2x)y′+(1−2x)y =0 on (0,∞).

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Q: y" + y = 2x

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Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: Find the solution to the IVP.y = cscx – ycotx' y(÷)= 1 ysinx = x+ 2 ysinx = x + 1- I 2 ycscx = x +…

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Q: x(x – 2)y" + 2(x – 1)y' – 2y = 0

A: Solution: x(x-2)y"+2(x-1)y'-2y=0 Solve using the series method: A linear homogeneous ODE with…

Q: 3) Find the particular solution of the DE y" = 12x² if y(0) = 1 and y'(0) = 2.

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Find the solution to the initial value problem y'=x²-, y(2) = 3.

A: Solution of the initial value problem

Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: x(1-х)у" - Зу' + 2у %3D0

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Q: Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water…

A: We are entitled to solve one question at a time and up to 3 sub-parts only. Please post other…

Q: ye2xdx ye2x. (4 + e2x)dy

A: The given equation is ye2xdx=4+e2xdy The given differential equation can be solved by converting it…

Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

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Q: (x³ – 9x² + 16x – 144)y²dy = (2x² – 1)e4Ydx - -

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Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: . Find the general solution of (³ + 2y*)y' = 3ya² in implicit form f(x,y) = c. When y(0) = 1, what…

A: We have given differential equation  x3+2y4y'=3yx2…

Q: Give a particular solution for y" – 2y' + y = 1+x2

A: Given that a differential equations - y" -2y' +y = ex/1+x2.   We know that integration of 1/(a2 +x2)…

Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: Solve for the particular solution of the non-homogeneous DE. 2y'' +y' = 3

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Q: 3. 2y" + у' - 3 А. 3 В. Зх C. 3x D. x?

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Q: 10. y"" + y" = 3 А. 3 В. Зх C. D. 3x?

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: Find a homogeneous LDE with constant coefficients that has y=-1+3x²e* as a particular solution.

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: 2y" + y' = 3

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Q: ) Give a particular solution for y" – 2y' + y = 1+x² *

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Q: Find the general solution of ylty = 2xcosx -cosX %3D

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Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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Q: what is the general solution of y (1 + 3x ) y - v ? Oy = 4 + 3x + Ce %3D = 4 +3z + Ce" 4 + 3x + Ce…

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Solve for x,y,z:  3x +2y − z = − 1  − 2x − 2y +3z = 5 5x +2y − z = 3

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Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: Find the general solution of the given second-order rerential eque 5y" + y = 0 y(x) = %3D

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Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

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Q: Solve for x,y,z if x+ 2y + 2z=0 2x + y + 2z = 0 2x + 2y + z = 0

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Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: 5. The particular solution of y' + y = y¯² when x = 0,y = 2 is

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Q: What are the largest steps you take to solve -4y, y(0)=1 dt (without getting an overflow!) using the…

A: (a) Given the IVP dydt=-4y, y0=1. The solution to this equation is given by yt=e-4t---1. The Forward…

Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy