Solve the problem. Find C(x) if C'(x) = k and C(9) = 40. A C(x) = 2x 3/2 + 31 B C(x) = 2 x 3/2 + 31 C(x) = 2x 3/2 + 22 D C(x) = x 3/2 + 22

Q: Solve the initial-value problem using the method of undetermined coefficients. y" + 5y' – 6y = 8e2x;…

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Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: Find the particular solution that satisfies the initial condition. x3y'+2y=e1/x^2, y(1)=e

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Q: Solve the initial value problem using the method of undetermined coefficients.  y"+4y'+4y=(3+x)e-2x,…

A: The given intial value problem is given by,

Q: Find the general solution of: y(x°+x*)dx - x(x³+ y-)dy = 0

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Which of the following is true in solving the initial value problem=x³—4—3e³¹,y=1whenx=0 ? A --4x-e³…

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Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: 5. Solve xdx + ydy а? (хdу-ydx) x2+y2 using exact D.E method.

A:

Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: 3) Solve the initial value problem : dy 4x5 4096 3x2 у(16) - 1 %3D %3D dx 5/2

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Find the general solution of y" – 3y' + 2y 1+e-x°

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Q: (2 marks) The general solution of the 3y = 0 equation (6xy + e')y' + xe* + is

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Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

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Q: solve the initial value problem. dy/dx + 3x2y = x2, y(0) = -1

A: Given differential equation is dydx+3x2y=x2 Comparing it with the general linear differential…

Q: What is the general solution of xy(xy³ – 1)dx + x²(1+xy)dy= 0 ? A 2x°y3 -3x2= Cx? B 2x³y5-3x² = c ©…

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Q: (b) Solve the initial value problem with seperation of variables and give your solution in the form…

A: Solve differential by using variable separable method

Q: Solve the initial value problem 2x(y+1)dx - ydy = 0, where x = 0 and y = -2

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Q: Obtain general solution of the D.E. y' + (1/3)y = e*yª A 1/y³ = e* (c – 3y) B 1/y³ = e* (c – 3x) с)…

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Q: Find the function f(x) by solving the initial value problem. f'(x) = ex - 2x ;   f(0) = 2

A: Given : f'x = ex-2xf0 = 2

Q: Solve the initial value problem. y dy dx = 9x ex, X The solution is y(x) = 9x ex - 5x. y(1)=9e-5

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Q: Find a particular solution for: y" - 3y' + 2y = te*

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Q: Solve the initial value problem using the method of indefinite coefficients. d'y d²y -5+4y 16x+ 20e"…

A: Given that the differential equation is d2ydx2-5dydx+4y=16x+20ex with y(0)=0, y'(0)=1. The axillary…

Q: Solve the initial value problem below. x²y" – - 3ry' + 4y = 0, y(1) = F 3, y'(1) = – 1 y =

A: Homogeneous Linear differential equation :   An equation of the form…

Q: Find the general solution using the method of undetermined coefficients. dx +7x=8e° dt -41

A: Answer

Q: 1. Find the general solution using variation of parameters. y" – 4y + 4y = (x +1)e²r

A: Solve by using variation of parameters.

Q: Find f ( x) by solving the initial value problem. f'(x)=e^(x)-4x;f(0)=3

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Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: xy' – y = 2x lnx

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Q: Solve the initial value problem. dv = + x, x > 0; y(1) = 5

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Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: Solve the given initial-value problem. x1' = 2x1 – x2 – 4x3 + 2e¬t x2' = 2x1 – 4x3+ 3e¬t X3' = x2 –…

A: Given: The initial-value problem, x1'=2x1-x2-4x3+2e-t x2'=2x1-4x3+3e-t x3'=x2-2x3+e-t such that…

Q: 3. Solve the initial value problem dy 3x2 + 4x + 2 y(0) = 3, dx 2(y – 1) and determine the interval…

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Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: Solve for the general solution * (4xy+3y – x) dx + x (x + 2y) dy = 0 x' (4xy² + 4y – x) = c x²…

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Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

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Q: 2. Solve the initial value problems using separation of variables. a. x' = t²x² , x(0) = 1 x(t) = t…

A: Given equation is dxdt=t2x2            (i) By using separation of variables,…

Q: d®y dæ 3 y (0) y' (0) 1 y" (0) = 0 ||

A: Let us consider the differential equation L[D]y=Q(x) Particular solution for the differential…

Q: Give the general solution of: dw/dx + (4w)/x = x3

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Q: Correct. Solve the given initial value problem. ○x6y² - xy³ = 12 | x³y² − y³ = −4 x³y² + xy³ = -4…

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Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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Q: Solve the initial value problem f'(x) = vx +,f(1) = 2.

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Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: Solve for the general solution. d³x dx -7. - + 6x = 0 dt3 dt

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Q: OBTAIN THE GENERAL SOLUTION (x - 1) dx - (3x - 2y - 5) dy = 0

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Q: solve y'' -4y' +4y =(12x^2 -6x)e^2x using variation of parameters given initial conditions; y(0)=1…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.