4(a)Verify that the equation y = Inx – Iny is an implicit solution of the TVP, ydx = x(y+ 1)dy y(e) = 1 (b) Consider the VP, test whether it is exact and solve it. x(x- y)dy= =(3xy– y²)dx y(-1) = 1

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Q2: Find General Solution (YGS)to the equation (Y4-1) Y=COS(2x)

A:

Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

A:

Q: Find the solution for following variable separable equation: x² (dx/dy) = y - xy , y(1)=1

A: The main objective is to solve the given variable separable equation.

Q: Solve this separable equations starting from y(0) = 2:  (1 + x)y′ = 2y

A:

Q: Verify the exactness of the given function (1+ex/y)dx+ex/y(1-x/y)dy=0 and then write the complete…

A: Solution: The objective is to find the general solution of the given differential equation

Q: Conduction equation Solve the heat Uxx = Ut -U; U = u(x, t)

A: uxx=ut-u

Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

A:

Q: (D2 -3D+2) y = e sin (e") - 2

A:

Q: Solve this linear IVP,        xlnx dy/dx + y= 2lnx,                           y(e)=2

A:

Q: 6z dy (78)a

A:

Q: Solve csc(x) – 2 = 0 on [0, 27]

A: Let's find.

Q: p" +2y' – xy = 0 n(x)= e

A: Given

Q: Using the basic formulas and change of variables, integrate the following: 1. S (3x3-1)2 2. Sdx xp*…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the solution to the Bernoulli equation: dy/dx + 2y/x = -x²y³

A: Introduction: One of the earliest differential equations to be solved was the Bernoulli equation,…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: du Solve dt 6u+3t e if u(0) = 2. U =

A:

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Solve (x − y − 1) dy − (x + 3x − 5) dx = 0

A: Rewrite the differential equation as                 dydx=x+3y-5x-y-1

Q: d’y - 2 y = 5x' + In(x²). dx

A:

Q: 3. Solve the DE: Y'=e2x+ 3y.

A:

Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: Q2) Solve (y+ysin x) dx - (cosx- 2xy +) dy = 0

A: Given differential equation is  y2+ysinxdx+-cosx+2xy-1y2+1dy=0 Comparing it with Mdx+Ndy=0, we get,…

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: (b) Solve the IVP (3xy – y²)dx = (xy – x²)dy y(-2) = 3 - %3D %3D

A:

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

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.