Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

Q: 7. Find the dy/dx of * y = In sin 5x

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Q: The solution of following Differential Equation dy sec²y+x tan y = x³ , is %3D dx

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Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: s.fx 5. x3 sin 3x dx

A: We have to find the indefinite integral

Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: 5 sin“(3t) dt

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: 1 of these 2 differential equations: dx dy O and (2x sin y +y) dx + (x² cos y + x)dy = 0 What are…

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Q: Find the general solution of y'= sin²xcosy.

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Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: 15 dy dt 2-

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Q: State the order of the given ordinary differential equation. (sin 8)y" - (cos 0)y' = 9 Determine…

A: Find your answer below

Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: Find dy/dx at the given point. 7x2y4=9-x2-9y  at (0,1)

A: Given: 7x2y4=9-x2-9y We have to find the dydx at (0,1)

Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: -Solve Bessel's Equation of order zero point x = 0 + xy = 0 around

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Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

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Q: 5. Solve dy dy + y = 2sin(3x) dx - dx? using the method of undetermined coefficient.

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Q: 1. Find the dy/dx of (2 Points) OY OY- 30"

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Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: Find dy/dx at the given point 6x2-5y3=2x-5y at (0,1)

A: First differentiate the equation and then substitute the value of x as 0 and y as 1.

Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: 11. Find dy/dx of In(x² + y²) + 2 arctan

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the equivalent differential equation for all tangent lines of the parabola y = x^2

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Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

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Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

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Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: What is the differential equation of the orthogonal trajectories of x3 = Cy?? (1) 3xdx + 2ydy = 0…

A: Given x3 = Cy2

Q: 1- Find the equation of the tangent to the 2(x2 + y2)2 25(x2 - y?) at (3,1) 2- Find dy/dx for y =…

A: (1) given equation is                                              2x2+y22=25x2-y2,   at (3, 1)…

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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Q: х2 9 dy + sinx - у %3D0 dx

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Q: dy Obtain general solution of- 3/xy dx

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Q: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: Obtain the general solution to the equation. 3. dx - (у — 2ху)dy

A: Topic - differential Equation

Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: Obtain the differential Equation from the family of ellipses centered at (h.k) whose semi-major axis…

A: Here h,k are parameters ,not constant.

Q: dy - 1 = siny dx

A: Given : dydx-1=siny To Find : solution of Given DE

Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions

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.