Find the particular solution to the differential equation: dy = 3x² cos² y. sSolution passes through the point (0, 4 ) dx Oln(cos² y) = x³ + 1 Oy = tan-' (x³) Oy = tan- (x³ + 1) | Cannot be determined

Q: Find the particular solution that satisfies the initial condition: Differential equation: 2xy' - ln…

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Q: Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus,…

A: We have to check Q(x)=Ce3x+1 is solution of given differential equation.

Q: 2. What is the integrating factor of the differential equation (x² -y²)dx + (x² - 2xy)dy = 0?

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Q: Find the general solution of seperable differential equation dy/dx=x3y2

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Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: What is the general solution of the differential equation y" +4y= tan 2x? Oy C1 cos 2x + C2 sin 2a -…

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Q: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

Q: Find the particular solution to the differential equation. 4y2 dx = 3x2 dy    when x = 4, y = −1

A: The objective is to find the particular solution of the differential equation.

Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

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Q: By using variation of parameters, what is a possible value for u' for the differential equation y' +…

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Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: The universal solution of the differential equation below may be found by substituting y=zx. Hence…

A: Given that                       x2 dydx = y (x+y)   hence we have to find the solution of d.E

Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

Q: Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential…

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Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

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Q: The diffeterctial equation is y²dx+ 3xZy² dx + dy=0

A: In the given question we have to find the value of the constant c at the point (2,1) when we solve…

Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

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Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: [cos y + 1]dy + [tanx (siny + y)]dx = [sin y cos x + y cos x]°dx gettyimages When:x = 0;y=

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Q: The solution of the given differential equation for y(1.5) is h=0.1 interval value. Calculate by…

A: Euler's method uses the formula, yn+1=yn+hf(xn,yn) to perform the iterations.

Q: I. dy tan(x) dx Cos (x) + x²

A: Given equation is dydx=tanxcosx+x2   What is the best way to solve the First Order Differential…

Q: x³y"+xy'+4y = cos (2 ln x) bulunuz.

A: See the attachment

Q: 3ydx What is the general solution to the differential equation 3dy + = y*(2x*)dx ?

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Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

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Q: y' cosx f. -=cos y

A: The given differential equation is,y'cos2x=cosy

Q: Find the particular solution to the differential equation: dy dx 3x2 cos? y. Solution passes through…

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Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

Q: 2. Consider the differential equation y' -()y = 2+G) t If y(0) = yo, find the particular solution to…

A: Explanation of the solution is given below...

Q: Find the general solution of the differential equation = 6 tan(5y) using separation of variables. dx…

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Q: (2 + tan2x)(1+е"У)dx — е У tan x dy %3D 0 = 0 %3D

A: Given differential equation is 2+tan2x1+e-ydx - e-ytan x dy = 0,   yπ2=0

Q: Use separation of variables to find the general solution of the differential equation. y- dx 4…

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Q: Find a particular solution for the differential equation y" – 2y' = 2+ 5 cos x using the method of…

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Q: A population (in thousands) grows according to the differential equation dy e ky(L-y), where the…

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Q: The general solution for the flowing differential equation is (3x²+ycosx) dx +(sinx-4y )dy =0

A: The equation is given by: 3x2+ycosxdx+sinx-4y3dy=0 The equation is of the form Px,ydx+Qx,ydy=0…

Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

A: solution:-  The given differential equation is  y''+4y=cos3x The auxiliary equation of above…

Q: Find the general solution of the differential equation using any method          y′ = √( 1 − cos )

A: Find the generla solution of given differential equation y'=1- cos x

Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: The differential equation formed by eliminating arbitrary constants a ,b andc: y = ax + bx + cx + 8…

A: In this question, we have to find the differential equation by eliminating parameters.

Q: Solve the differential equation by variation of parameters. y"+ y = sin(x) %3D x cos(x) y(x) =…

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Q: Determine the general solution of the given differential equation. y(4) + 2ylI + 2yl/ -x = 3e" + 2e™…

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Q: ,Find the two values of k for which y(x) = ekx is a solution of the differential equation %3D…

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin æ +…

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Q: Find the particular solution to the differential equation: dy/dx=3x^2cos^2y. Solution passes…

A: The given differential equation is in variable separable form. We solve the differential equation by…

Q: xydx + 2(x2 +2y)dy=D0; when x= 0, y= 1

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Q: The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O…

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx

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.