The solution if the initial value problem xy' = y+x sin(x), y(7)=0 is given by %3D Select one: O y(x) = -r(cos(x) + 1) %3D O Cannot be determined from given information. O y(x) = 7+x cos(a) %3D O y(x) r sin(x) %3D

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: y" – 2y' + 2y = e2= (cos r – 3 sin r) (undetermined coefficients) %3D

A:

Q: Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) +…

A: Given that  Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0 and Implicit solution : ln(x2+18)…

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 O A.…

A: solution of differential equation

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: If f(z) = 2 sin I +3 cos z, then f'(x) = %3D

A:

Q: 6. Find Sin 5x (b) y = THcos 5x dx

A:

Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 16) cos(y) dy = 0 is given by In(x? + 16) +…

A:

Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: If h (x) = sin (4x) then h 0. V3 V3 2 II

A: Given that hx=sin4x.

Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

A:

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

A:

Q: If y=tan(arcsec/x), then dy/dx is x – 1 A 2(x-1) sec2(arcsec/x) B sec2(arcsec/x) 2x D none of the…

A:

Q: (b) S – cos(x) + 5 sec x cos x dx

A: This is is integration question

Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: (1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I =…

A:

Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

A:

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: Find f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

A:

Q: (f) y" - y' + 2y = 3e + 4 cos 2x

A: Consider the differential equation y''-y'+2y=3ex+4cos2x. To find the general solution of given…

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

A:

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

A:

Q: #17 Determine the equations of function graphed below.

A: According to question We have to calculate the equation of the graph.

Q: What is the solution of 2 tan (cos x) = tan (2 cscx). (а) 0 (b) 4 (c) 2 (d) 6.

A:

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

A:

Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

A:

Q: (4) [xsec? x dx

A: 4- Given- ∫xsec2x dx To Find- The value of the above integral. Identity Used- Using the by part…

Q: The approximated value for e using the Maclaurin series expansion coasidering a true relative error…

A:

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.