Q1:- Solve the following Des 4) y" – 4y' + 3y = 4x+3e" 2x

Q: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

A: Solve for the particular solution of the non-homogeneous DE. y'' + y = 2x

Q: 3. Solve the particular solution (D² + 3D + 5)y = 5e¬*sin2x using D- operator method.

A:

Q: 8x²y" + 10xy' – (1+ x)y = 0

A:

Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: y" - 6y' + qy 2,

A:

Q: y" + y = 2x

A:

Q: Q.1 Solve the IVP: y" + 3y' + 2y = 686(t) with conditions: y(0) = 0, y'(0) = -1.

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1…

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Find a general solution valid near the origin: (x²+4)y" + 2xy' - 12y = 0

A:

Q: Solve the DE x²y"+xy'+ (x²-÷) y=x³/2, given that Yı=x-1/2sinx and y2=x-1/2cosx are two solutions of…

A: Given the given DE is x2y"+xy'+x2-14y=x32. y1=x-12sinxy2=x-12cosx

Q: 1 Oy' = %3D xsiny+2sin2y

A:

Q: 4. y" - 5y' + бу %3 -sin(2x)

A:

Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: Suppose we are given y₁ (x) and y2(x) (with y₁ y2), which are two different solutions of a…

A:

Q: 14.Show that any separable equation M(x)+N(y)y′=0 is also exact.

A: Given: Mx+Nyy'=0

Q: 1nd the general and definite solutions of the diIference equations

A:

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

A:

Q: y" – 2y' + y = –3 – x + x²,

A:

Q: 7. Eliminate a and b from the equation y =- In(ar +bx) where a,beR-(0}

A: q-7 eliminate a and b from the equation y=12lnax2+bx  this can be written as 2y=lnax2+bx⇒e2y=ax2+bx…

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: 4. Solve the following equation by backward Euler's method and also trapezoidal method: 1 1+t² y'…

A: Introduction: There are many iteration tools that are used to solve an initial value problem…

Q: 2. Modify the following equation into Clairaut's form. Hence obtain the associated general…

A: Introduction: Clairaut's equation is a first order higher degree ordinary differential equation. It…

Q: Find the general solution of y" – y' – 2y = cosh 2t.

A:

Q: Use Secant method to find to find solution accurate to within 10 for the following problem. (i).…

A: Given function is  (i) f(x)=3xex Here x0=1, x1=2 f(x0)=f(1)=3(1)e1>0 f(x1)=f(2)=3(2)e2>0 Since…

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: Solve this equations by using homotopy analysis methods y"+y' ^(2)=0 with initial condition v'(0)=2

A:

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

A:

Q: Solve the particular solution (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

A: We find the particular solution of  (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: 5- Find the particular solution for: 2e2x – y = xy', x = 1 when y = 6 %3D

A:

Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

A:

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

A:

Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

A:

Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: 8. Obtain the particular Solution by satisfying the conditions indicated. y' = x exp (y - x²); when…

A:

Q: Apply the appropriate method to solve the Cauchy-Euler equation 2x²y "+ 5xy'+ y = x² – x

A:

Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: Solve the follawing systen. 2 x, - 5x - cost dt dx2 b) by using the method of unde termined…

A: Given system is dx1dt=2x1-5x2-costdx2dt=x1-2x2+sint First, let us solve corresponding homogenous…

Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

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.