|Example 10.27. Find an approximate series solution of the simultaneous equations dx/dt = xy + 2t, dy/dt = 2ty +x subject to the initial conditions x = 1, y = - 1, t 0. %3D %3D

Q: 5y' + xy = x2 + 5

A: We solve the differential equation by finding Integrating factor method. For the standard first…

Q: 1.4 1+ axb -dx ebr dt 1.5 da – ebt

A:

Q: Explain in detail: classification of Partial Differential Equations.

A: We have to explain the classification of partial differential equations.

Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

A:

Q: Example 4: Solve i) y" + 7y' + 10y = 2x + 3e*

A: the given differential equation isy''+7y'+10y=2x+3exfirstly complementary function CF and then PI…

Q: 3. Given y = (1- V2x); Find dy/dx %3D du

A:

Q: If y = 3 then dy/dx = 4+x O -6x/ (4 + x² )2 O 3x/ (4 + x² )² O 6x/ (4 + x² )2 O -31 (4 + x? )?

A:

Q: dt 1 - sec t

A: Given that: ∫dt1-sect

Q: 3:30 A3. If y = e2x+5 then y' = %3D LA) 2e2x+5 (b) e2x+5 (c) 5e2x+5 (d) e2

A: Given query is to find the derivative of the expression.

Q: 9y" + 30y' + 25y = 0, and y(3) = 9, y (3) = 3. %3D

A: For the complementary solution consider the quadratic  9m2+30m+25=0 The equation has repeated roots…

Q: (3) (2x – 3y – 2)dx + (6(2x – 3y) – 2)dy = 0. - - %3D

A:

Q: how did this equation Hx = exp P (ny + ). ož = vi[exp (o,) – 1] turned into this equation 1 In Hy =…

A:

Q: Find y'' for y = 5x +4. 25x2 y'= - O A. 2 (5x? +4) 1 y" = O B. 4 (5x2 + 4) 20 y" = OC. (5x? + 4)…

A:

Q: Problem. Show that S {₁ 【 (s − 2)(s − 3)(s — 6) J L-1 -6)} = 1/2 ²² - e³t + e

A:

Q: Solve xy" + y = 0.

A:

Q: y" + x?y = 0.

A: Given :     y"+x2y=0                         ......1 Let yx=∑aixii=0∞ is the solution of given…

Q: Parabolas with axis parallel to the x-axis

A: Differential equation, parabola parallel to x-axis.

Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

A:

Q: 4. (3x – y)2 = 6x + 2y + 23 @ (1,-2) 5. x(x² – y²) = 3 @ (-1,2)

A: 4) (3x-y)2=6x+2y+23, @(1,-2) 5)x(x2-y2)=3, @(-1,2).

Q: Find the differential equation of the family of parabolas with vertex at (1, 3) and axis parallel to…

A: To Find: The differential equation of the family of parabolas with vertices at (1, 3) and axis…

Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

A: Given

Q: Find the differential equation of the family of parabolas with vertex and focus on the x-axis. Draw…

A: The equation of parabola with vertex at h,0 and focus at h+a,0 is,…

Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

A:

Q: Differentiate. y = In [e 7X (x5 + 5) (x° + 4x) ] d [in [e 7* (x° + 5) (x° + 4x)]] = ] TX (x5 + 5)…

A:

Q: Solve the linear differential equation dy y 2x2 - dx

A: Given differential equation is dydx - yx = 2x2