3. Find an explicit solution of the given initial-value problem. dx 4(x + 1), x(7/4) = 1 dt 2 dy y sin x, y( 2) dx 1.

Q: Find the solution of the given initial value problem in explicit form. () T sin(2x) dx + cos(9y) dy…

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Q: Solve the given initial-value problem. (y? cos(x) – 3x?y – 4x) dx + (2y sin(x) – x³ + In(y)) dy = 0,…

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Q: Solve the given initial-value problem. (y² cos(x) - 3x²y - 6x) dx + (2y sin(x) − x³ + In(y)) dy = 0,…

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Q: 1. Solve the initial value problem: dy 2xy): 1 + cos x y(y + sin x), y(0) = 1. dx %3D 1+ y?

A: The given differential equation is  11+y2+cosx-2xydydx=yy+sinx,  y(0)=1

Q: Solve the initial-value problem (4y−cos y) dy /dx −3x2 = 0, y(0) = 0

A: 4y-cosydydx-3x2=0 On simplification, we get ⇒4y-cosydydx=3x2⇒4y-cosy dy=3x2 dx Now integrating on…

Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(9y) dy =…

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Q: Solve the given initial-value problem. dx = y - 1 dt dy = -8x + 2y dt x(0) = 0, y(0) = 0 |-cos( v7t)…

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Q: Find an explicit solution of the given initial-value problem. dx 8(x2 + 1), dt IT 1 %3D 4

A: We need to find explicit solution.

Q: Solve the initial value problem. dx 3. t2 + 3tx = t* In t + 1, x(1) = 0 dt

A: To solve the initial value problem.t2dxdt+3tx=t4 ln t+1,     x1=0

Q: Find an explicit solution of the given initial-value problem. (4)- dx 7(x² + 1), dt x = 1 %3D

A: To find an explicit solution of the initial - value problem : dxdt = 7x2+1 , xπ4 = 1

Q: dy y- 1 dx -1' y(2) = 2

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Q: and the differential equation M (x, y)dx + (sin x cos y – xy - e-)dy = 0 is exact. |

A: It is exact differential problem

Q: Solve the initial-value problems dy y(1) = 2 dx dy = cos t + 1, dt 2

A: To solve the given initial value problems

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

A:

Q: Find the function y = y(x) which satisfies the separable differential equation dy/dx = 8+11x/(xy^2)…

A: Given differential equation is dydx=8+11xxy2y2dy=8+11xxdx Integrate both sides.…

Q: . Find the general solution to y + 2x = 5y³. dy . Solve the initial value problem of (sin x) = y cos…

A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

Q: Solve the seperable differential equation for. dy 1+ x ;x > 0 xy5 dx Use the following initial…

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Q: - (a) Find the solution of the given initial value problem in explicit form: dy y dx y(1) = 1

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Q: Find the particular solution of the differential equation dy/dx+ycos(x)=4cos(x) satisfying the…

A: Given differential equation is,

Q: Find an explicit solution of the given initial-value problem. dy = y sin x? , y(-2) = ; dx

A: The given equation is: dydx=y2sinx2, y-2=13

Q: Solve the initial-value problem. 3 dy + 3t²y = 2 cos(t), y(¹) = 0 dt

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Q: Solve the initial valve problem au - y' sin x, y (0) = 3 dx = y° sin x, y (0) = 3

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Q: Solve the given initial value problem for y=f(x) 1) dy/dx=3x-2 where y=2 when x=-1

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Q: Find the solution of the given initial value problem in explicit form πT sin (2x) dx + cos (3y) dy =…

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Q: Solve the separable differential equation dy e*ye®* dx with initial condition y(0) = 1.

A: Given : dydx = exyeex

Q: Solve the initial-value problem cos y + (1 + e^−x)sin y dy/dx = 0, y(0) = π/4

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Q: 6. Verify that y(x) = /E+ 9 is a solution of the initial-value dy problem 1 and y(0) = 3. 2y dx ||

A: To verifyy(x)=x+9 is  a solution of the given IVP dydx=12y

Q: Solve the given initial-value problem. (y? cos(x) – 3x²y – 2x) dx + (2y sin(x) – x³ + In(y)) dy = 0,…

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Q: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

A: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

Q: solve the initial value problem. (x+1)dy/dx+ 2y = x, x >-1, y(0) = 1

A: Write the equation as linear differential equation.

Q: Find an explicit solution of the given initial-value problem. () - 1 dx 3(x2 + 1), dt X =

A: Given query is to find the solution of the differential equation.

Q: For differential equation dy/dt = (y2-2)arctan(y) sketch the graphs of the solutions satisfying the…

A: For differential equation dydt=(y2-2).arctan(y) sketch the graphs of the solutions satisfying the…

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: Solve the given initial-value problem. (y2 cos(x) – 3x²y – 4x) dx + (2y sin(x) – x³ + In(y)) dy = 0,…

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Q: Solve the initial value problem dy/dx + y = 2 sin x, y(0) = 1.

A: Given differential equation is Comparing it with  we get The integrating factor of the…

Q: Find explicit particular solutions of the initial value problems in Problem 2 dy dx - cos? y, y(4) =…

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Q: Find the function y = y(x) (for > 0) which satisfies the separable differential equation %3D dy 10+…

A: Use variable separable method to solve

Q: Find the general solution to the initial value problems: (i) dx = 0, where x(0) = 1, 2x -3t dt (ii)…

A: We need to solve the initial value problems given by dxdt+e-2xe-3t=0, where x(0)=1dydt=(t-6)ey,…

Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

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Q: Find the solution of the given initial value problem in explicit form. 77 ㅠ sin(2x) dx + cos(8y) dy…

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Q: Solve the initial-value problem shown below: 6ty dy t2 +1 y (0) = 1/2 . dt Give an exact formula for…

A: Given differential equation is Integrating both sides, we get

Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

A:

Q: The solution of the following exact initial value problem (y cos x – xy sin x)dx + (x cos x – 1)dy =…

A: The solution of the differential equation is defined as the function that satisfies the equation. In…

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(9y) dy = 0,…

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Q: 3. Solve the initial Value Problem x dy +(y-cos x)dx = 0, y )=0 %3D

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Q: Solve the initial-value problem. +3dy + 3t²y = 8 cos(t), y(t) = 0 dt

A: We have to solve this initial value problem.

Q: =e*", y(0)=1. dx Find the solution of the initial value problem

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Q: 3. Find the solution of the initial-value problem d'y_3dy +2y=e* dx y(0)=1, y'(0) = 0 dx Using…

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Q: Find an explicit solution of the given initial-value problem. dy y (2) = 2 %3D dx x2-1

A: An equation which involves the derivative or differential coefficient is called differential…

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.