1- Solve the problem P.D.E. Uz = Uxx + sin(nx) + sin(2nx) 0

Q: Determine the value of k such that k y=(1-sinx) * is a solution to 2y'=y³cosx

A:

Q: Let R = {(x, y) E R² | In y <¤<1n1<y <e} and let S be the surface defined by the vector function…

A: x=u+vy=evv=ln y1≤ev≤ee0≤ev≤e10≤v≤1ln y≤u+v≤1ln y≤u+ln y≤11≤u≤1-ln y1≤u≤1-v

Q: 13x (b) sin 12

A: NOTE: Refresh your page if you can't see any equations. . use the formula

Q: 6. sec (sin-1 x)

A: Interconversion

Q: 6. Find dy dx of cos y - 2xy + 3x = 2x sin x

A:

Q: 4x x*e*dx (2sin dx V4-x2

A: We can solve all the intregration problems with tha mathod of substitution. In substitution we use a…

Q: Find dy/dx for x*+siny = x'y

A:

Q: de cos² 0

A:

Q: хр X UIS X,SO + (cos³x)y = 1 Кр

A:

Q: 11. 2y" + 3y + y = t² + 3 sin t

A:

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

A:

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

A:

Q: x' - x? = t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5…

A: We will use Mathematica to solve these. Each question has multiple initial value problems. 6 (a):…

Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

A:

Q: 1 = x²y" + xy' + cx? - +»v=o x>0 ,V1=X sinx , and y =y,v. Which of the following quations satisfied…

A:

Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: 3. 2√3 sin 2x = -√3, [0, 2π)

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Find dy dx if sin(x + y) = tan(xy)

A:

Q: If x*y" + xy' + (x? - y= 0 x >0 ,V1=x 2 sinx 3D0 and y =y,v. Which of the following equations…

A:

Q: 1. cos x sin* x dx

A:

Q: Prove that fx" cos(2x)dx=sin(2x)-[x n sin(2x)-x-¹ sin(2x)dx. Do not use Table Entries. H

A: