Find the general solution using Reduction of Order: y''+y'=cos 3x

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

A:

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: evaluate using Integration by Parts.

A:

Q: 2x cos(2x)dx

A: Given : ∫2xcos2xdx

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: Find integral.

A: Given: Let I=∫2x cos x2 dx To Find: To evaluate the given integration.

Q: Find the general solution to the ODE using the method of Variation of Parameters: y" + y= cos² x

A:

Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

A:

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

A:

Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: Find the differential of z = sin²(5x) + ev

A:

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: Use linear approximation or differentials to approximate cos (1.6)

A:

Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

A:

Q: Determine whether the differential equation is separable. y'= 4x cos (y)-xy Separable Not separable

A:

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

A:

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: Verify the integration formulas ∫sech x dx = tan-1 (sinh x) + C

A: To evaluate ∫sech x dx

Q: 5

A:

Q: y" + 2y' = sin 2x ||

A:

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: dy cosx+ ysin x =1 dx

A:

Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: Ssin (2x)cos(2r)dx

A:

Q: Find the differential of w = ln /x² + 3y² + 2z²

A: Here we use chain rule of differentiation to find the required differential. According to chain rule…

Q: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

A:

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

A:

Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

A:

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

A:

Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

A:

Q: -1 | tan *xdx

A: The given integral,       ∫tan-1x dx

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

A:

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

A: Given                   y43= sinx cosx1+2.lnx

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Integrate using substitution: [x* cos(x' )dx

A:

Q: Evaluate / e*cos(x)dx using integration by parts-

A:

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: 2. f x cos² x dx

A:

Q: Solve for the differential of y when y- sinax. x= and dx O o o

A:

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

A:

Q: 4. Use integration by parts to evaluate (2x - 5) cos(5x - 2)dr.

A: