2. Verify that r = Cie +C2 is a solution to a" – r' = 0. Find C1 and C2 so that r satisfies x(0) = 1 and a'(0) = 10.

Q: 3, Find the poner sertes solution in poners of (x-1) of *最+y=o; 0 2 +2y=0j つ4 4(メー)-4(メー)れ +…

A: Given that xy''+y'+2y=0 Take y=c0+c1(x-1)+c2(x-1)2+c3(x-1)3+c4(x-1)4+c5(x-1)5+.. Take the derivative…

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A:

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

A:

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

A:

Q: For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution…

A: In this question, we have to use the uniqueness theorem and find the appropriate values of y0

Q: Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х +…

A: OPTION D IS CORRECT.

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: Please see the answer in step 2

Q: 1. Find the solution of the PDE with the prescribed auxiliary conditions by the method of separation…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: 2. xyy' = 1+ y? ; when x = 2, y = 3

A: Given xyy' = 1+y2 and  x=2 >>> y=3

Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

A:

Q: 4. Find the General and Particular solution of dy -8 sin 4x ; y = 6 when x = 0 dx dy

A:

Q: 1. Show that y(x) = c; sin 2x + c₂ cos 2x is a solution to y + 4y = 0.

A:

Q: Find the general solution of the DE y’’ = xsin(x)

A: Topic = Differential equation

Q: y" – 2y' = e*

A:

Q: Find a particular solution to y" + 5y' + 6y = lte".

A:

Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

A: Solution

Q: x²y" +xy' – y = T

A:

Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

A:

Q: 3. Show that the equation (6xy – y*)dr + (4y + 32² – 3ry²)dy = 0 %3D is exact. Hence solve the…

A: Given that  The differential equation is  To solve the differential equation with intial condition

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

A:

Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

A:

Q: Use the annihilator operator (not undetermined coefficient) for the right hand side and use it with…

A:

Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

A:

Q: 2nd Case (IBVP Summary) (Ut = 1.5uxx, 0 0 Ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0<…

A:

Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

A: An explicit solution is any solution that is given in the form y=y(x)

Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

A:

Q: Solve for the particular solution of the following non-homogeneous DE. y” – y’ = 2sin 2x

A:

Q: 6. Using the u-substitution u = x2+ 1, solve the initial value problem dy 4.r Vr2 +1 and y(0) = 0 dr…

A:

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: Find the complete solution of the DE y"- y'=4e¯* +3e* with the initial conditions that when x = 0, y…

A:

Q: Show that this function satisfies the initial conditions yp(to) =0 and y'(to) =0, so it is a…

A:

Q: +2. =0 by Find the solution of the PDE dx? dy² variable separable method

A: Given problem is :

Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: O DE Linitial condelim) dy -48-7x y)= 1 +2

A: we have to find the diifferential equation dydx=4x2-7x3y2+2    with initial condition y(1)=1

Q: 3- Find non-zedo solution ofs dy

A: we need to solve the given first order nonlinear differential equation. The given equation is…

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: Show that y=lnx is a solution of xy’’+y’=0 on interval (0,∞) but is not a solution on interval…

A:

Q: Solve the initial value problem Ut + 2uz = 1, x € R, t e R u(0, x) = e¯*, x € R. %3D

A: The differential equation is given as ut+2ux=1 The Lagrange equation is given as dt1 = dx2 = du1 On…

Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: 9. Ify,(x)= sin 2r and y, (x) = cos 2x are two solutions of y"+ 4y 0, show that y, (x) and y, r) are…

A:

Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: 2. Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) =Q

A:

Q: Verify that the function y(r) = 2, is a solution of the initial value problem dy + 2y = 3y, v(0) =;…

A:

Q: Show that this function satisfies the initial conditions y,(to) =0 and y'(to) = 0, so it is a…

A:

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

A:

Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

A:

Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

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.