4. Find the solution of the vibrating string problem ᎧᎳ ᎧᎳ + əx² dy² with the boundary conditions W (0, y) = W (1, y) = 0, ᎧᎳ 1 ㅠ = cos(- 2πx) - 3 sin(5x), ду W(x,0)= = 0, 0≤x≤1, 0≤ y ≤ 1, 3π -(x,0) = cos(- +3πx). 2 Trigonometric formula cos(A + B) = cos A cos B - sin A sin B.

Q: Solve the D. E. to the I. V.P. (1 +x² + y² + x?y²)y' = y², 2. y(1) = 1

A: The solution is given as

Q: 2x a) y" + 4y' + 4y x2 b) (D* + 8D2 - 9)y = x2 + sin 2x

A:

Q: 5) y"-y'-2y=x+cosx

A:

Q: What is the general solution of (1 + a2) y' = x*y %3D Oy"-3ay + 1 = C O ay - 3ry + 3y% tan-1 æ + 1 =…

A:

Q: 3) dx 2 ·0 CSC csc y dx + sec ³x d y = 710185²³ 3x dup бу

A: Here we have to find the solution of the differential equation cosecydx+sec2xdy=0.

Q: i) tanzy dy sin3xdx

A: As we know that  (i)  tan2y=sec2y-1(ii) ∫sec2ydy=tany+C(iii) sin3x=3sinx-sin3x4(iv)…

Q: d'y The general solution of the differential equation dy +2- 5y 0 is dx Ay Ce-2+6)x+ Czel-2-6)x y=…

A:

Q: 5. Exact Difle rential Equation: 3ry -4y' +6dr + (r° – 6x°y² - 1kty =0

A:

Q: Let u and uz be two solutions of the nonhomogeneous equation Ly] = y" + +y= sin(t). Then y = u - uz…

A: There is a theorem that which I am stating below:

Q: 4. The complementary solution of following equation y"" - 3y" + 4y' - 2y = ex + cosx, is (a) c₁e+…

A:

Q: 3 -2 3 2. A fundamental set of solutions of x' = 1 х is: 1

A:

Q: 31) y +y, = 2cos(1), y, + y, = 0, y, (0) = 0, y,(0) = 1.

A:

Q: Find the general solution of y""- 6y"+21y'- 26y=0 3x A y=c,e"+c,e cos 2x +c,e"sin 2x 2x В…

A:

Q: y" + 4y' + 3y = sin (e*) %3D

A: follow next step

Q: 3) CSC 4) Sin 3 xdx + 2y cos 3x dy = 0 12

A:

Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: tan - de 3 3 sec

A: According to Bartleby's guidelines we can solve only 1 question at a time. Here's the solution for…

Q: 4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

A: Find partial derivative using chain rule then put values of x ,y,z in obtained expression then put…

Q: The solution of у" + у 3D 0, у(0) — 0, у'(0) — 1 is y(a) = (A) cos x (B) sin x (С) 1 — е ӕ (D) 1– eª…

A:

Q: 5) Find y' if x + cosy = Vx + sinx + xy – 1

A: Given

Q: 3) a) Solve:' 4x³y +4x?y(2)_ sxy'+2y=0 Co,0) on

A:

Q: 7. Find the general solution of (Dʻ + 2D’ + 10D²)y = 0.

A:

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: 8.2 Making the change of variable z=cos(x) in the equation y" - y' cotx - y sen²x = 0,, the equation…

A:

Q: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

A:

Q: E. Direction: Analyze the Venn diagram below and find the complements of each set. 3. Let W =…

A:

Q: (D-9)y 3e" +x-sin 4x. 3 1 A. y C,e*+C,e* +e* +÷x- sin 4x 25 -3x 8 3 1 B. y Ce* +C,e-* +e* -x- sin 4x…

A:

Q: A particular solution of y" + 2y' + 5y = e sinx 4 elsinxcosx) 13 13 2 sinx + cosx) 65 a. b. ex (355…

A: we will find the required.

Q: 9. A particular solution of y" +9y = 3 sec 3x is (a) z = cos 3x ln | sec 3x + x (b) zcos 3x ln | sec…

A:

Q: 1) d कर dy + 4x3 + 2y = 0,

A:

Q: 1. Find f(x, y) obeying = - sin(x)y and f(0, y) = }(y +2)². %3D %3D

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

Q: 11. Evaluate * d²y dy - 2 + 5y = –17sin2x dx2 dx y = (C,e* + 68 |cos2x +(Cze* + 17 sin2x 15 y =…

A: