Solve step by step in digital format please explain each step thanks! 2²u 1 ди Solve the heat equation for = əx² adt u(0, t) = 0, u(1,t) = 0,_ u(x,0) = 5sin (5x)——sin(³x)

Q: How could the 1D heat equation represent physically?

A: We know that the heat energy of a body with uniform property is represented as; where c is the…

Q: provide

A:

Q: 5. 6. Solve fo e-t sint dt. dt. t Solve fe-t. -t sint t

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

Q: Let Find A-¹ and use it to solve where where x₁ = -24 and 2 -0 = A = 4 -3 4 4 AX = B B = (²3) X = -…

A: We see,        So, Determinant of A = |A| = 4×4 - (-3)×4                                        = 16…

Q: Solve the ODE of variable coefficients first changing this to constant coefficients x²y" – 4xy' + 6y…

A:

Q: Find the solution. dy +y%3= dx 1 1+e* (A y = ce*+e*In (1+e*) B y = ce¯ - e-*In(1-e*) (c) y = ce-…

A:

Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

A: Solution: A first-order Bernoulli ODE has the form of y' + p(x)y =q(x)yn Rewrite the form of…

Q: solve et (l-t)? with y coJ=2 and y'Co)=6

A: We have to solve

Q: Solve by lagrange method, find the general solution to the ODE y = x(y' - x cos(x))

A: Given differential equation is  y=xy'-xcosx⇒y'=xcosx+yx⇒y'-1xy=xcosx which is of the form y'+Py=Q.…

Q: ubstitution Suggested by the Equation y′ + 1 = 4e^−y sin x

A: Given differential  equation is dydx + 1  = 4 e-ysinx ey dydx+ ey = 4 sinxLet  ey  = v eydydx =…

Q: 2. ye*dx + e*dy = 0

A:

Q: Find y' and y". y=2sin4x-cos(8x-1)

A: Let's find.

Q: solve using the appropriate method. y' + yx= sin x

A:

Q: y′= (6xe^(6x)) X (cos^(2) (6y)) a) Write the equation in an integrable form by separating it into…

A: Solve using variable separable method.

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

Q: 3 (x-2) y'= y + 2(x-2)

A:

Q: Evaluate -o (i +1) 3° ui = 0

A:

Q: Find y' if 7 y² + sin (3x) = 12-y f

A: Here we can find the y' in the below steps, using implicit differentiation.

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

Q: Y''+4y=cosx find solution

A: We have to find the solution of the differential equation y''+4y=cosx. Consider the homogeneous part…

Q: Find y'. sin t y = 8 + t %3D y' = %3D Find y'. 2 sin 0 + 9 cos 0 y = %3D sin 0 – cos 0 y' = %3D

A:

Q: RICCATTI 1. y' =2 tanx secx y₁ = sec x -y²sinx

A: This is the question of the differential equations. Application of Ricatti and Bernoulli'es…

Q: Find y' if 7 y² + sin (3x) = 12-yf

A:

Q: х -14х + 5 3. x(х - 1)(х — 5) - dx

A:

Q: cot (7x+5). sin ( 3x+2) csc ( 7x+5) dx

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

Q: Apæ'/s-1/Apy/s-1 %3D

A: The given equation is: xy=λρx1s-1λρy1s-1

Q: ху' %3D у (1 — х tan x) + x? cos х x) + x² COS X

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: The surface given by z = x² – y? is cut by the plane given by y the point (1, 3, –8). 3x, producing…

A:

Q: x+1 Solve y'=- y +1

A: Differential equation