Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

Q: 4. Find the particular solution of y(x² + y²)dx + x(3x² – 5y²)dy ;where x = 2 and y = 1. -

A:

Q: (x² + y²)dx – xydy = 0 -

A:

Q: Find the general solution: y" – 2y" + 4y' – 8y = sinh 2x

A:

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

A:

Q: I Solve the differential equatons when X= (x+y) dx +(2xy+xh 3x) dy=o 1. Y= 2

A:

Q: The solution of y" + y = 0 with initial conditions y (0) = 1 and = 2 is RIN

A:

Q: y" + 2y' + y = x at x = 0, y = -3, and x = 1, y = -1

A:

Q: Given y'+y = 0, y(3) = 2. Solve this initial value problem for x = 3(0.5)5 using Euler's %3D !!…

A:

Q: Q3) Use Euler's method to estimate y(0.02) ey-x 1+ e2y y(0) = 1 ( h=0.01) .What is the error in the…

A: Given ; h = 0.01 y(0) = 1

Q: The general solution of y" - 2y' +y= e* cos(x) is

A:

Q: Q2] (A) Find the general solution to ONLY ONE of the following differential Mations (1) (sec(y))2…

A:

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

A:

Q: yy' – xcos(x²) = 0, y(0) = -2

A: We have to find the particular solution of the given initial value problem.

Q: 3. Find the general solution of y" – 3y + 2y = cos (e~-).

A: We use the method of variation of parameters to find the solution of y''-3y'+2y=cose-x First we find…

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

A: Topic = Differential equation

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ;0sx<1 ;y(0) = 1 ; h = 0.5 dx

A:

Q: Let y'=3t and y(0)=0 Approximate y(4) using Euler's method with a step size of 2. Solve exactly…

A:

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: xy²dx + e*dy = 0

A: Given differential equation is xy2dx+exdy=0

Q: Q5:al Using the Runge-Kutta method, solve x = 0.2 when h = 0.2. dy = x + y² with the initial…

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

Q: 1. Solve for y3 using the method of successive approximation. dy = x + y; y(1) = 1

A:

Q: Find the particular solution that satisfies the initial condition(s). y = C, + C2 In x xy" + y' = 0…

A:

Q: Find the complete solution of yn+4y=ex sin2x

A:

Q: Find the solution to the Bernoulli equation. y = 2(3x+ y)2 – 1; x= 0,y=1 O 4tan-1(3x+ y) = 8x + T…

A: The solution is given as

Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: How do I find the general solution of y''- 2y'= e^x * sinx using the method of variation of…

A: y''-2y'=ex sin x Auxiliary Equation: m2-2m=0⇒m1=0, m2=2 Complementary function  :  y=c1+c2e2xthis…

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

A:

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

A:

Q: 3. Find the general solution of y"-3y'+2y = e2* cos x [using variation of parameters]

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: Find the particular solution determined by the initial condition. ds 16t2 + 5t – 5; s(0) = 100 dt

A:

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

A:

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ; 0 <x<1 ;y(0) = 1 ; h = 0.5 dx

A: If dydx=fx, y, yx0=y0 then Euler's method states that  yn+1=yn+h·fxn, yn Given : h=0.5, x0=0, y0=1,…

Q: Find general solution of (x − 4y − 3)dx + (−x + 6y + 5)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

A:

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: Use Euler method to approximate the value of y(0.1), given y' - 4y = 3x2, y(0) = 5 with Ax = 0.02

A:

Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

A:

Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: 3. Find the general solution of y"-3y'+2y=e2* cos x [using variation of parameters]

A: See solution below

Q: Solve using separable differential equations Vydx + (1+ x)dy = 0, when x = D 1, у %3D 4

A:

Q: Xy"+y=0. solve by forbenius method.

A:

Q: Find the particular solution of xy' - 4y = 0 ; initial condition y = 2 when x = 1.

A:

Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…