Consider the initial value problem T = ¤1 + 3x2 I½ = 3x1 + #2 with the initial conditions a (0) = 5 and r2(0) = 1. What is the solution for z (t)? %3D Select one: O 1(t) = 3e4t + 2e_2t O 1 (t) = 2e*t + 3e-2 O 1:(t) = 3e 4t – 2eª O 1 (t) = 3e 4t + 2eª O 1(t) = 3et – 2e 24

Q: Find the general solution to the equation xdx + -dy= 3dy O x=/2y+ Cy-2 O xy= 2y + C O y = 2x3 + C…

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Q: 1 Find the general form of solution of the first order equation U + 2u, = (x – 2t)u + 2t2 + 3tx -…

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Q: 14. x2 – 2x – 8 <y

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Q: x1 = X2 = Solve the following initial value problem: d 15 4 4et ²-(4 15 ) ² + ( 16 ) = dt 64 -16et…

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Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: (15) Verify that is a particular solution of Show all work to receive full credit. Yp=-4x² y" - 3y'…

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Q: y(4) + 18y" + 81y = 0

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Q: Q2// find the general solution 1 + 4y) dx + 4xdy = 0 3-4x2 - x + 4

A: The differential equation is given as 1x3-4x2-x+4+4ydx+4x dy = 0 Compare it with M dx+ N dy=0 Here M…

Q: y-3y" + y' + 5y =

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Q: 11. In the function y = 3x2 - 3, y is replaced by y and then y is replaced with y +2 ; the new…

A: Given:     Function y=3x2-3   Here y is replaced by 12y       substitute y=12y      12y=3x2-3…

Q: If a(b + x) + y = z, solve for b (= - y) atz ziy-a a (z-v) a (y + 2) a (v (2) 20 B +x

A: To find the value of b.

Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: (c) Solve the following IVP by separating variable. 2(y - a)da + (3a + 4r + b)dy = 0 Using initial…

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Q: -x+y+3z = 3 x+2y-z 0 3x+2y %3D -5z = -2

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Q: #8: Consider the following matrices. --3--03] Problem #8: Find an elementary matrix E such that EA =…

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Q: true or false: a. y=3lnx a solution to y(4)-16y=0 b. y=3e-2x a solution to y(4)-16y=0

A: Part a,Given,y = 3 INx a solution to y(4) - 16y = 0

Q: y²dx+x(x+y) dy=0 A xy² = c(x+2y) x²y=c(x+2y) xy² = c(2xy) x+y²=c(2xy) B C D

A: Given: The equation is y2dx+x(x+y)dy=0. To find: The correct option for the solution of the given…

Q: 2y Solve (3x² + e ²¹) dx + (2xe ² − 4y) dy = 0 A B x² + xe ²y = 2y² = C 2y - D x³ + xe ³y - 2y³ = C…

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Q: Find the general solution of (y-zx)p+(x+yz)q=x2+y2

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Q: (³ +2w)® 6. Find dy/dx, given the following: y = /2x–4 3(3=° +2) (z"+2) O (E) None of the choices…

A: Formula ddxuv=vdudx-udvdxv2 ddx(xn)=nxn-1 ddx(x)=12x 6. Given y=(x3+2x)32x-4 Differentiating with…

Q: 5. The function y₁=+1 is a solution of (1-2-2³)+2(1+)/-2yy=0. Find the general solution.

A: PLEASE NOTE: There is a slight  typing mistake in this question ,the differential equation should be…

Q: Solve the initial value problem (y² + yx)dx + x²dy = 0, y(4) = 1. Select one: O y+ 2x = x²y 9(y +…

A: Given differential equation y2+yxdx+x2dy=0 Simplify it…

Q: Find the general solution to 3x²y²dx + (2x³y + 4y³)dy = 0

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Q: y²dx + x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) © xy²=c(2xy) C D x+y²=c(2xy)

A: Given differential equation  y2 dx +xx+y dy=0

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.