3. (D² + 4)y = 10 cos 3x. ANS. Y = -2 cos 3

Q: 2. Find the general solution of the given differential equation. dr + rsece = cos0 do

A: The given differential equation is; dr/d(theta) + r sec(theta)=cos(theta).

Q: (D² – D – 6)y = 0; when x = 0, y = 2, y' = 1. |

A:

Q: A student was solving a separable differential equation and got this far: jdy-(x* 3) dx -(x²3)dx…

A:

Q: Q.2: Solve the higher differential equation below; yiv – y = 2 cos x

A: yiv-y=2cosx The above differential equation can be written as D4-1y=2cosx      , D=ddx The Auxiliary…

Q: 6. Solve the differential equation by using the method of variation of parameters: y"+ y = sec x…

A: The general solution of the second order linear differential equation y''+py+qy=fx is y=yc+yp where…

Q: Solve the given differential equation by separation of variables. dy ху + бу — х — 6 - - dx ху — 5у…

A:

Q: Show the process in solving this differential equation

A:

Q: 1. Xy" + (y)2 - 2xy' = Q

A: We will find solution of given differential equation as shown below

Q: x²y² dy — 3у +1 dx

A:

Q: Find the general solution to the differential equation: y' = 9° %3D

A: The given differential equation is: y'=9x   We know that; ∫axdx=axlna+C

Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

A:

Q: An L-R-C circuit has the following differential equation: (q = charge on capacitor) with q (0) = 1…

A:

Q: 4. y = Cie+ C2e + Cse, where y(0) =0, y'(0) = 1, y"(0) = 2 %3D

A:

Q: . Solve for the differential equation and get the particular solution. 1. ye dx (9- e3*)dy; x 0 y= 1

A: Simplify the given equation to separate the variables.     Take integration on both sides of the…

Q: Solve the differential equation. dy 9xvy dx for y+ 0

A:

Q: xdy - (y + x² cos(x)) dx = 0

A: xdy-y+x2cosxdx=0xdy-ydx-x2cosxdx=0xdydx-y-x2cosx=0dydx-yx=xcosxFirst order linear diff. eq.

Q: dy (5) Solve the differential equation by variable separable y = csc y dr

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: 2. Solve the differential equation dy sin x dx 2 y-cot x

A:

Q: 7. (D² + 4)y = 6 sin x. ANS. y = 2 sin x. %3D

A:

Q: Make an appropriate substitution to find a solution of the equation dy/dx = sin(x – y). Does this…

A:

Q: Solve the given differential equation by separation of variables. dy 5x +3y dx 1 5x

A: The given differential equation is                                                     dydx=e5x+3y…

Q: A student is solving a separable differential equation and gets this far: ly=(x²3)dx What is the…

A: Integration is used to determine the bigger value by adding all the small parts. While…

Q: Q-7. Solve the differential equation y = 1+ fip +..... for | 1 |< 1. dz dz

A:

Q: dy 5) Solve the differential equation by variable separable x*y- dr

A: Given differential equations is x3y2dy/dx=e-y

Q: dy Solve the differential equation for y if (1+9x²) 1 %3D dx

A:

Q: Solve by rewriting the differential equation as an equation for dy , for x21 with y(3) =1 dx dx The…

A:

Q: e'sin2 xdx + e2Ycosxdy= ycosxdy 1

A: Given differential equn is eysin2xdx+e2ycosxdy=ycosxdy⇒(eysin2x)dx+(e2ycosx-y…

Q: 1 dy 1 )? dx Solve the differential equation ( 2x sec 2y II

A:

Q: 2ss" + (s')² = 0 %3D

A: Explanation of the answer is as follows

Q: (2) Solve the differential equation dy sin x, y(0) = 3. dx

A:

Q: (D² + 3D – 4)y = 18 e2×.

A: Complete solution of differential equation is :  Y = CF +PI

Q: 4. Solve for the general solution of the differential equation using homogenous equation. [x cos?…

A: A homogeneous differential equation is an equation containing a differentiation and a function, with…

Q: blve |x+ ye* |dx - хе* dy —D 0, y(1)-0

A:

Q: 3. The dearee of the differential equation below is: * (2) (2)* + sin(2) + 1 = = 0 dx

A: Question 3,Given,            d2ydx23+dydx2+sindydx+1=0

Q: Solve the given differential equation by separation of variables. dy 5x + 3y dx

A:

Q: 5. Find the general solution of the differential equation using GeoGebra (D² +9)y=2 sina

A: General equation of differential equation.

Q: find the solution of the differential equation     dy / dx = y / (y-x)  with y(5) = 2

A:

Q: dy/dx+(2/x)ydx=3dx

A:

Q: 5) Solve the differential equation given as dy (dz) ² dy +2- y dr² dr

A:

Q: 2xe2"dy + (e?y – 12x?)dx = 0

A:

Q: Find the value of the constant(s) so that the function x (t) = emt is a solution of the Differential…

A:

Q: (D³ + 3D² – 4D – 12)y = 0

A: To solve the given differential equation.D3+3D2-4D-12y=0

Q: D. Solve the given differential equation by variations of parameters. 1. y" + y = cos² x

A:

Q: Solve the given differential equation by separation of variables. dyxy + 5x - y – 5 dx xy - 2x + 6y…

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

Q: dy 2. Find the particular solution to the differential equation = 8x3 + sin x if the solution dx…

A:

Q: Q1. Solve the differential equation of following 1. (x² + 1) = dy dx y

A:

Q: 3. Solve the differential equation by variation of parameters. y" + 3y + 2y = cos(e*)

A:

Q: Solve the differential equation dy /dx = 6 x sq. / 2 y + cos y

A: By separating the variables, we get

Q: Q4- Solve the following differential equation: (1+r)dy + (y-tan-¹(x)) dx = 0

A:

Q: 2. Solve the differential equation dy 2y-cot x tan dx

A: