- y" – 4y' + 13y = e2*cos3x

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

A:

Q: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: Given

Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

A:

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

A:

Q: Solve for the general solution of the below differential equation. y" + 3y' + 2y = cos x

A:

Q: 13 Find solution of non-homogeneous differential equation (D* +1)y = sin (3x)

A: Find complementary function and particular integral

Q: 20.Find the particular solution of the differential equation x (+1) - x-2y, given x -1 when y = 3

A:

Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

Q: III. dy y³ dx x²y-xyz

A: Sol:- y' =y3x2y-xy2Substitute y=vx, v is a function of xxv' +v=v21-vRewrite in the form of a first…

Q: 10. Find the general solution to a sixth-order linear homogeneous differential equation for y(x)…

A: We first write the possible roots of the auxiliary roots  of auxiliary equation of  the sixth order…

Q: 5. By using separable differential equation, solve the initial-value problem 2x(y + 1)dx -y dy= 0,…

A:

Q: determine the general solution to thegiven differential equation. y′′′ − y′′ + y′ − y = 0.

A:

Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

A:

Q: (9) Show that the solution of the differential equation y + y = -6ye» with y(0) = -1 is (e* –…

A:

Q: [6] Find the solution of the first order ordinary differential equation (1– 3y2) dy – x sinx dx=0, y…

A:

Q: Find a general solution of the second-order nonhomogeneous differential equation y" - 2y' + y =…

A:

Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: 2. Solve the differential equation: (y² + xy°)dx + (5y² – xy+ y° sin y)dy = 0 by finding an…

A:

Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: Find a particular solution yp of the nonhomogenous differential equation y(3) + y' = x sinx + x²e* +…

A:

Q: y = G, cos 3x – C, sin(-3x)

A: The general solution of a differential equation is y = c1cos(3x) - c2sin(-3x) We need to find the…

Q: 4. Solve the differential equation 2x(2x – 1)- (x + 1)+y = 0 using the method of Frobenius. dx2…

A: 2x2x-1d2ydx2 +x+1dydx +y=0                       eq.(1) To solve by Frobenius series.

Q: 2. Test the exactness and obtain the general solution of the differential equation: 2+yexy y' =…

A:

Q: 5. Solve the differential equation with method of undetermined coefficients. y" + 2y' – 3y = x + cos…

A:

Q: 2. Solve the differential equation using undetermined coefficients satisfying the given conditions.…

A:

Q: 5. In the differential equation (1+3xsin ykdx-x cos ydy = 0, we let the substitution %3D

A: Follow the procedure given below.

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: - ydx + (x ++ Vxy )dy= 0

A:

Q: 3 2 2. x" - y' + 4x y = 0, x > 0; y,(x) = sin x

A: Given:          xy''-y'+4x3y=0 , x>0 y1(x)=sinx2    Use reduction of order method   let…

Q: 6. Find the general solution of the following differential equation using variation of parameters.…

A:

Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

Q: 1.) Find the general solution to the first order differential equation given below. -3x 3xe 2x y' 4y

A: In the given question we have to solve the given ordinary differential equation of first order and…

Q: 3. Solve the Euler-Cauchy differential equation d' y dy - 3x+4y=ln² x – In x dx dx?

A:

Q: 1. Given the differential equation: y" = cos(5x). Determine its general solution. A. 125y = -cos(5x)…

A:

Q: 2- Find the solution of these differential equations : 1. (x – y) = x + y dy dr

A:

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

A:

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

A:

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 2. Solve the first order linear differential equation y'+2xy = x, with initial value y(0) =1.

A:

Q: 5. Solve the second order differential equation, dx2 + 4+ 4y = cos2x, given y = 4 and dy :3 when x =…

A: 1f(D2) cos ax = 1f(-a2) cosax 1D X =∫X dx

Q: 4ху Find the solution to the differential equation dx which passes through the point (0, e). (In…

A: We first separate the variables:dydx=4xylny10lny10dyy=4xdxThen we integrate both…

Q: 3. Solve the Euler-Cauchy differential equation d²y dy 3x +4y= ln² x – In x dx² dx

A: Given an Euler-Cauchy differential equation, x2y"-3xy'+4y=ln2x-lnx Re-writing it in the standard…

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

A:

Q: 4- Solve the following differential equation: (1 + x²)dy + (y − tan−¹(x)) dx = 0 -

A: Given: The differential equation is 1+x2dy+y-tan-1xdx=0 To find the general solution of the given…

Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Given xdy-y+xy3(1+lnx)dx=0

Q: (20) Determine the complete solution of the differential equation y" + 4y = 2cos2x subject to…

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

Q: 2. | Determine the general solution of the given differential equation y" -6y" = 3- cos x

A: The solution is given as