y" – 4y' + 13y = e2* cos 3x

Q: Solve the differential equation y' = x(y – 3) with initial condition y(0) = 1.

A: Solution :-

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

A:

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

A: Given

Q: Solve the differential equation dydx = 5cos(x)y

A:

Q: 2. Form a Differential Equation for the given equation y = 2 cosx + 5 sinx by eliminating the…

A:

Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

A:

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

A: Find complementary function and particular integral

Q: Find the general solution of the first-order differential equation                       y′ = 2x√(1…

A:

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied 1 sin 2 1…

A:

Q: The value of 'a' for the exact differential equation (1+ +)dz - dy is O - 4 O 2 O -2

A:

Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

A:

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

A:

Q: The particular solution of the following nonhomogeneous differential equation y"-2y' +y = x² +e-* by…

A: Given nonhomogeneous differential equation:y"- 2y'+ y= x2 + e(-x)  ;

Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

A:

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: x³y"+xy'+4y = cos (2 ln x) bulunuz.

A: See the attachment

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

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Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

A:

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

A:

Q: A solution for the differential equation is y = eux A1 sin (vx) + A2 cos (vx), where m and n are…

A: We will find out the required values.

Q: Obtain the differential equation associated with the primitive y = Ae3x + Be2x + Ce*.

A: Given differential equation is we have to obtain the differential equation associated with the…

Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

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: xcosydy + sin2ydy – dx = 0

A:

Q: 4. xy = x cos( y/x)+y

A:

Q: x²y" - xy'+ 5y = 0

A:

Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 & Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

Q: Verify that the indicated expression is an implicit solution of the given first-order differential…

A:

Q: Find the general solution of the first-order differential equation                       y′ cos x2 +…

A: The first-order differential equation is y'cosx2+ycosx2x=secx2

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: Solve the Euler-Cauchy differential equation dy -3x + 4y = dx In?x - Inx

A:

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: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: Solve the first order differential equation. dy - y ln(y ecos x) dx = y sin xdx

A:

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

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

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Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² +…

A:

Q: Solve the differential equation dy/dx=5-x/y with the inital condition y(6)=-4.

A: We have to solve

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: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin æ +…

A:

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: dy 47. = cos cos 2x, y(0) = 3 dx

A:

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: Find the special solution of ele differential equation. = 20x - 4x3 dy dx y with the initial value…

A:

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

A: The solution is given as